The second law of thermodynamics is an expression of the universal law of increasing entropy. In simple terms, it is an expression of the fact that over time, differences in temperature, pressure, and density tend to even out in a physical system that is isolated from the outside world. Entropy is a measure of how far along this evening-out process has progressed. The laws of thermodynamics, in principle, describe the specifics for the transport of heat and work in thermodynamic processes. ... The zeroth law of thermodynamics may be succintly stated as: If two thermodynamic systems A and B are in thermal equilibrium, and B and C are also in thermal equilibrium, then A and C are in thermal equilibrium. ... The first law of thermodynamics, a generalized expression of the law of the conservation of energy, states: // Description Essentially, the First Law of Thermodynamics declares that energy is conserved for a closed system, with heat and work being the forms of energy transfer. ... The third law of thermodynamics (hereinafter Third Law) states that as a system approaches the zero absolute temperature (hereinafter ZAT), all processes cease and the entropy of the system approaches a minimum value. ... In thermodynamics, the combined law of thermodynamics is simply a mathemtical summation of the first law of thermodynamics and the second law of thermodynamics subsumed into a single concise mathematical statement as shown below: Here, U is internal energy, T is temperature, S is entropy, P is pressure, and V... Thermodynamics (from the Greek θερμη, therme, meaning heat and δυναμις, dunamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... Ice melting - classic example of entropy increasing[1] described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice. ...

The most common enunciation of second law of thermodynamics is essentially due to Rudolf Clausius: Rudolf Clausius - physicist and mathematician Rudolf Julius Emanuel Clausius (January 2, 1822 – August 24, 1888), was a German physicist and mathematician. ...

There are many statements of the second law which use different terms, but are all equivalent. (Fermi, 1936) Another statement by Clausius is: In thermodynamics, an isolated system, as contrasted with a closed system, is a physical system that does not interact with its surroundings. ... Insert non-formatted text hereInsert non-formatted text hereInsert non-formatted text hereInsert non-formatted text hereInsert non-formatted text hereInsert non-formatted text hereInsert non-formatted text hereInsert non-formatted text hereInsert non-formatted text hereInsert non-formatted text hereInsert non-formatted text hereInsert non-formatted text hereInsert non...

Heat cannot of itself pass from a colder to a hotter body. In physics, heat, symbolized by Q, is defined as transfer of thermal energy [1] Generally, heat is a form of energy transfer associated with the different motions of atoms, molecules and other particles that comprise matter when it is hot and when it is cold. ...

An equivalent statement by Lord Kelvin is: William Thomson, 1st Baron Kelvin, OM, GCVO, PC, PRS, FRSE, (26 June 1824 – 17 December 1907) was a mathematical physicist, engineer, and outstanding leader in the physical sciences of the 19th century. ...

A transformation whose only final result is to convert heat, extracted from a source at constant temperature, into work, is impossible.

The second law is only applicable to macroscopic systems. The second law is actually a statement about the probable behavior of an isolated system. As larger and larger systems are considered, the probability of the second law being practically true becomes more and more certain. For any isolated system with a mass of more than a few picograms, the second law is true to within a few parts in a million.^[1] The U.S. National Prototype Kilogram, which currently serves as the primary standard for measuring mass in the U.S. It was assigned to the United States in 1889 and is periodically recertified and traceable to the primary international standard, The Kilogram, held at the Bureau International des Poids et...

Overview

In a general sense, the second law says that temperature differences between systems in contact with each other tend to even out and that work can be obtained from these non-equilibrium differences, but that loss of heat occurs, in the form of entropy, when work is done.^[2] Pressure differences, density differences, and particularly temperature differences, all tend to equalize if given the opportunity. This means that an isolated system will eventually come to have a uniform temperature. A heat engine is a mechanical device that provides useful work from the difference in temperature of two bodies: In thermodynamics, thermodynamic work is the quantity of energy transferred from one system to another. ... In thermodynamics, an isolated system, as contrasted with a closed system, is a physical system that does not interact with its surroundings. ... A heat engine is a physical or theoretical device that converts thermal energy to mechanical output. ...

Heat engine diagram

During the 19th century, the second law was synthesized, essentially, by studying the dynamics of the Carnot heat engine in coordination with James Joule's Mechanical equivalent of heat experiments. Since any thermodynamic engine requires such a temperature difference, it follows that no useful work can be derived from an isolated system in equilibrium; there must always be an external energy source and a cold sink. The second law is often invoked as the reason why perpetual motion machines cannot exist. Image File history File links Carnot-engine. ... Image File history File links Carnot-engine. ... A Carnot heat engine is a hypothetical engine that operates on the reversible Carnot cycle. ... Conservation of energy also known as the first law of thermodynamics is possibly the most important, and certainly the most practically useful, of several conservation laws in physics. ... In thermodynamics, an isolated system, as contrasted with a closed system, is a physical system that does not interact with its surroundings. ... This article or section should include material from Parallel Path See also Perpetuum mobile as a musical term Perpetual motion machines (the Latin term perpetuum mobile is not uncommon) are a class of hypothetical machines which would produce useful energy in a way science cannot explain (yet). ...

History

See also: History of entropy

The first theory on the conversion of heat into mechanical work is due to Nicolas Léonard Sadi Carnot in 1824. He was the first to realize correctly that the efficiency of this conversion depends on the difference of temperature between an engine and its environment. The history of entropy, essentially, is the development of ideas set forth to theoretically understand why a certain amount of functionable energy released from combustion reactions is always lost to dissipation or friction, i. ... Sadi Carnot Nicolas Léonard Sadi Carnot (June 1, 1796 - August 24, 1832) was a French mathematician and engineer who gave the first successful theoretical account of heat engines, the Carnot cycle, and laid the foundations of the second law of thermodynamics. ...

Recognizing the significance of James Prescott Joule's work on the conservation of energy, Rudolf Clausius was the first to formulate the second law in 1850, in this form: heat does not spontaneously flow from cold to hot bodies. While common knowledge now, this was contrary to the caloric theory of heat popular at the time, which considered heat as a liquid. From there he was able to infer the law of Sadi Carnot and the definition of entropy (1865). James Joule - English physicist James Prescott Joule, FRS (December 24, 1818 – October 11, 1889) was an English physicist, born in Sale, Cheshire. ... Rudolf Clausius - physicist and mathematician Rudolf Julius Emanuel Clausius (January 2, 1822 – August 24, 1888), was a German physicist and mathematician. ... The caloric theory is an obsolete scientific theory that heat consists of a fluid called caloric that flows from hotter to colder bodies. ...

Established in the 19th century, the Kelvin-Planck statement of the Second Law says, "It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work." This was shown to be equivalent to the statement of Clausius. Alternative meaning: Nineteenth Century (periodical) (18th century — 19th century — 20th century — more centuries) As a means of recording the passage of time, the 19th century was that century which lasted from 1801-1900 in the sense of the Gregorian calendar. ... The kelvin (symbol: K) is a unit increment of temperature and is one of the seven SI base units. ... This article is about Planck, the German physicist. ... A cyclic process is a thermodynamic process which begins from and finishes at the same thermostatic state. ... In thermodynamics a heat reservoir is considered as a constant temperature source. ...

The Ergodic hypothesis is also important for the Boltzmann approach. It says that, over long periods of time, the time spent in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e. that all accessible microstates are equally probable over long period of time. Equivalently, it says that time average and average over the statistical ensemble are the same. In physics and thermodynamics, the ergodic hypothesis says that, over long periods of time, the time spent in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i. ...

Using quantum mechanics it has been shown that the local von Neumann entropy is at its maximum value with an extremely high probability, thus proving the second law ^[3]. The result is valid for a large class of isolated quantum systems (e.g. a gas in a container). While the full system is pure and has therefore no entropy, the entanglement between gas and container gives rise to an increase of the local entropy of the gas. This result is one of the most important achievements of quantum thermodynamics. Fig. ... Quantum statistical mechanics is the study of statistical ensembles of quantum mechanical systems. ... Quantum entanglement is a quantum mechanical phenomenon in which the quantum states of two or more objects have to be described with reference to each other, even though the individual objects may be spatially separated. ... In the physical sciences, quantum thermodynamics is the study of heat and work dynamics in quantum systems. ...

Informal descriptions

The second law can be stated in various succinct ways, including:

• It is impossible to produce work in the surroundings using a cyclic process connected to a single heat reservoir (Kelvin, 1851).
• It is impossible to carry out a cyclic process using an engine connected to two heat reservoirs that will have as its only effect the transfer of a quantity of heat from the low-temperature reservoir to the high-temperature reservoir (Clausius, 1854).
• If thermodynamic work is to be done at a finite rate, free energy must be expended.^[4]

William Thomson, 1st Baron Kelvin, OM, GCVO, PC, PRS, FRSE, (26 June 1824 – 17 December 1907) was a mathematical physicist, engineer, and outstanding leader in the physical sciences of the 19th century. ... Rudolf Clausius - physicist and mathematician Rudolf Julius Emanuel Clausius (January 2, 1822 – August 24, 1888), was a German physicist and mathematician. ... In thermodynamics, thermodynamic work is the quantity of energy transferred from one system to another. ... The thermodynamic free energy is a measure of the amount of mechanical (or other) work that can be extracted from a system, and is helpful in engineering applications. ...

Mathematical descriptions

In 1856, the German physicist Rudolf Clausius stated what he called the "second fundamental theorem in the mechanical theory of heat" in the following form:^[5] Rudolf Clausius - physicist and mathematician Rudolf Julius Emanuel Clausius (January 2, 1822 – August 24, 1888), was a German physicist and mathematician. ... In the history of science, the theory of heat or mechanical theory of heat was a theory, introduced predominately in 1824 by the French physicist Sadi Carnot, that heat and mechanical work are equivalent. ...

where N is the "equivalence-value" of all uncompensated transformations involved in a cyclical process. Later, in 1865, Clausius would come to define "equivalence-value" as entropy. On the heels of this definition, that same year, the most infamous version of the second law was read in a presentation at the Philosophical Society of Zurich on April 24th, in which, in the end of his presentation, Clausius concludes:

This statement is the best-known phrasing of the second law. Moreover, owing to the general broadness of the terminology used here, e.g. universe, as well as lack of specific conditions, e.g. open, closed, or isolated, to which this statement applies, many people take this simple statement to mean that the second law of thermodynamics applies virtually to every subject imaginable. This, of course, is not true; this statement is only a simplified version of a more complex description. The Universe is defined as the summation of all particles and energy that exist and the space-time in which all events occur. ...

In terms of time variation, the mathematical statement of the second law for a closed system undergoing an adiabatic transformation is: In thermodynamics, a closed system, as contrasted with an isolated system, can exchange heat and work, but not matter, with its surroundings. ... This article covers adiabatic processes in thermodynamics. ...

where

S is the entropy and

t is time.

It should be noted that statistical mechanics gives an explanation for the second law by postulating that a material is composed of atoms and molecules which are in constant motion. A particular set of positions and velocities for each particle in the system is called a microstate of the system and because of the constant motion, the system is constantly changing its microstate. Statistical mechanics postulates that, in equilibrium, each microstate that the system might be in is equally likely to occur, and when this assumption is made, it leads directly to the conclusion that the second law must hold in a statistical sense. That is, the second law will hold on average, with a statistical variation on the order of 1/√N where N is the number of particles in the system. For everyday (macroscopic) situations, the probability that the second law will be violated is practically nil. However, for systems with a small number of particles, thermodynamic parameters, including the entropy, may show significant statistical deviations from that predicted by the second law. Classical thermodynamic theory does not deal with these statistical variations. A pocket watch, a device used to tell time Look up time in Wiktionary, the free dictionary. ... Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... In statistical mechanics, a microstate describes a specific detailed microscopic configuration of a system, that the system visits in the course of its thermal fluctuations. ...

Available useful work

See also: Available useful work (thermodynamics)

An important and revealing idealized special case is to consider applying the Second Law to the scenario of an isolated system (called the total system or universe), made up of two parts: a sub-system of interest, and the sub-system's surroundings. These surroundings are imagined to be so large that they can be considered as an unlimited heat reservoir at temperature T_R and pressure P_R — so that no matter how much heat is transferred to (or from) the sub-system, the temperature of the surroundings will remain T_R; and no matter how much the volume of the sub-system expands (or contracts), the pressure of the surroundings will remain P_R. Exergy is the maximum amount of work one can get from a system as it comes into equilibrium with a large reference environment. ...

Whatever changes dS and dS_R occur in the entropies of the sub-system and the surroundings individually, according to the Second Law the entropy S_tot of the isolated total system must increase:

According to the First Law of Thermodynamics, the change dU in the internal energy of the sub-system is the sum of the heat δq added to the sub-system, less any work δw done by the sub-system, plus any net chemical energy entering the sub-system d ∑μ_iRN_i, so that: The first law of thermodynamics, a generalized expression of the law of the conservation of energy, states: // Description Essentially, the First Law of Thermodynamics declares that energy is conserved for a closed system, with heat and work being the forms of energy transfer. ...

where μ_iR are the chemical potentials of chemical species in the external surroundings. In thermodynamics and chemistry, chemical potential, symbolized by μ, is a term introduced in 1876 by the American mathematical physicist Willard Gibbs, which he defined as follows: Gibbs noted also that for the purposes of this definition, any chemical element or combination of elements in given proportions may be considered a...

Now the heat leaving the reservoir and entering the sub-system is

where we have first used the definition of entropy in classical thermodynamics (alternatively, the definition of temperature in statistical thermodynamics); and then the Second Law inequality from above.

It therefore follows that any net work δw done by the sub-system must obey

It is useful to separate the work done δw done by the subsystem into the useful work δw_u that can be done by the sub-system, over and beyond the work p_R dV done merely by the sub-system expanding against the surrounding external pressure, giving the following relation for the useful work that can be done:

It is convenient to define the right-hand-side as the exact derivative of a thermodynamic potential, called the availability or exergy X of the subsystem, Exergy is defined differently in different fields of study. ...

The Second Law therefore implies that for any process which can be considered as divided simply into a subsystem, and an unlimited temperature and pressure reservoir with which it is in contact,

i.e. the change in the subsystem's exergy plus the useful work done by the subsystem (or, the change in the subsystem's exergy less any work, additional to that done by the pressure reservoir, done on the system) must be less than or equal to zero.

Special cases: Gibbs and Helmholtz free energies

When no useful work is being extracted from the sub-system, it follows that

with the exergy X reaching a minimum at equilibrium, when dX=0. Exergy is defined differently in different fields of study. ...

If no chemical species can enter or leave the sub-system, then the term ∑ μ_iR N_i can be ignored. If furthermore the temperature of the sub-system is such that T is always equal to T_R, then this gives:

If the volume V is constrained to be constant, then

where A is the thermodynamic potential called Helmholtz free energy, A=U-TS. Under constant volume conditions therefore, dA ≤ 0 if a process is to go forward; and dA=0 is the condition for equilibrium. In thermodynamics, the Helmholtz free energy is a thermodynamic potential which measures the “useful” work obtainable from a closed thermodynamic system at a constant temperature. ...

Alternatively, if the sub-system pressure p is constrained to be equal to the external reservoir pressure p_R, then

where G is the Gibbs free energy, G=U-TS+PV. Therefore under constant pressure conditions dG ≤ 0 if a process is to go forwards; and dG=0 is the condition for equilibrium. In thermodynamics, the Gibbs free energy is a thermodynamic potential which measures the useful work obtainable from a closed thermodynamic system at a constant temperature and pressure. ...

Application

In sum, if a proper infinite-reservoir-like reference state is chosen as the system surroundings in the real world, then the Second Law predicts a decrease in X for an irreversible process and no change for a reversible process.

is equivalent to

This expression together with the associated reference state permits a design engineer working at the macroscopic scale (above the thermodynamic limit) to utilize the Second Law without directly measuring or considering entropy change in a total isolated system. (Also, see process engineer). Those changes have already been considered by the assumption that the system under consideration can reach equilibrium with the reference state without altering the reference state. An efficiency for a process or collection of processes that compares it to the reversible ideal may also be found (See second law efficiency.) This article or section does not cite its references or sources. ... In physics and physical chemistry, the thermodynamic limit is reached as the number of particles (atoms or molecules) in a system N approaches infinity — or in practical terms, one mole or Avogadros number ≈ 6 x 1023. ... Chemical engineering is the application of science, mathematics and economics to the process of converting raw materials or chemicals into more useful or valuable forms. ... Exergy efficiency is also called second-law efficiency because it computes the efficiency of a process taking the second law of thermodynamics into account. ...

This approach to the Second Law is widely utilized in engineering practice, environmental accounting, systems ecology, and other disciplines. Engineering is the design, analysis, and/or construction of works for practical purposes. ... Environmental accounting can be considered either a subset or superset of accounting proper, because it aims to incorporate both economic and environmental information. ... Systems Ecology is a transdiscipline which studies ecological systems, or ecosystems. ...

Criticisms

Owing to the somewhat ambiguous nature of the formulation of the second law, i.e. the postulate that the quantity heat divided by temperature increases in spontaneous natural processes, it has occasionally been subject to criticism as well as attempts to dispute or disprove it. Clausius himself even noted the abstract nature of the second law. In his 1862 memoir, for example, after mathematically stating the second law by saying that integral of the differential of a quantity of heat divided by temperature must be greater than or equal to zero for every cyclical process which is in any way possible:^[5] In physics, heat, symbolized by Q, is defined as transfer of thermal energy [1] Generally, heat is a form of energy transfer associated with the different motions of atoms, molecules and other particles that comprise matter when it is hot and when it is cold. ... Absolute zero is the lowest temperature that can be obtained in any macroscopic system. ...

Clausius then states:

This statement, curiously, from one perspective, may be said to be equally valid to this very day. That is, owing to ambiguous nature of heat and temperature themselves, as they relate to sciences such as chemistry and particle physics, entropy is still an ambiguous quantity. As such, scientists are forever trying to find loop-holes in the second law^{[citation needed]}: In physics, heat, symbolized by Q, is defined as transfer of thermal energy [1] Generally, heat is a form of energy transfer associated with the different motions of atoms, molecules and other particles that comprise matter when it is hot and when it is cold. ... Fig. ... It has been suggested that the central science be merged into this article or section. ... Thousands of particles explode from the collision point of two relativistic (100 GeV per ion) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ...

Perpetual motion of the second kind

Before 1850, heat was regarded as an indestructible particle of matter. This was called the “material hypothesis”, as based principally on the views of Isaac Newton. It was on these views, partially, that in 1824 Sadi Carnot formulated the initial version of the second law. It soon was realized, however, that if the heat particle was conserved, and as such not changed in the cycle of an engine, that it would be possible to send the heat particle cyclically through the working fluid of the engine and use it to push the piston and then return the particle, unchanged, to its original state. In this manner perpetual motion could be created and used as an unlimited energy source. Thus, historically, people have always been attempting to create a perpetual motion machine so to disprove the second law. In physics, heat, symbolized by Q, is defined as transfer of thermal energy [1] Generally, heat is a form of energy transfer associated with the different motions of atoms, molecules and other particles that comprise matter when it is hot and when it is cold. ... This article or section should include material from Parallel Path See also Perpetuum mobile as a musical term Perpetual motion machines (the Latin term perpetuum mobile is not uncommon) are a class of hypothetical machines which would produce useful energy in a way science cannot explain (yet). ...

Maxwell's Demon

In 1871, James Clerk Maxwell proposed a thought experiment, now called Maxwell's demon, which challenged the second law. This experiment reveals the importance of observability in discussing the second law. In other words, it requires a certain amount of energy to collect the information necessary for the demon to "know" the whereabouts of all the particles in the system. This energy requirement thus negates the challenge to the second law. Moreover, to reconcile this apparent paradox from another perspective, one may resort to a use of information entropy, although this is considered questionable by some. James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and theoretical physicist. ... In philosophy, physics, and other fields, a thought experiment (from the German Gedankenexperiment) is an attempt to solve a problem using the power of human imagination. ... Maxwells demon is an 1867 thought experiment by the Scottish physicist James Clerk Maxwell, meant to raise questions about the possibility of violating the second law of thermodynamics. ... Claude Shannon In information theory, the Shannon entropy or information entropy is a measure of the uncertainty associated with a random variable. ...

Time's Arrow

Main article: Entropy (arrow of time)

The second law is a law about macroscopic irreversibility, and so may appear to violate the principle of T-symmetry. Boltzmann first investigated the link with microscopic reversibility. In his H-theorem he gave an explanation, by means of statistical mechanics, for dilute gases in the zero density limit where the ideal gas equation of state holds. He derived the second law of thermodynamics not from mechanics alone, but also from the probability arguments. His idea was to write an equation of motion for the probability that a single particle has a particular position and momentum at a particular time. One of the terms in this equation accounts for how the single particle distribution changes through collisions of pairs of particles. This rate depends of the probability of pairs of particles. Boltzmann introduced the assumption of molecular chaos to reduce this pair probability to a product of single particle probabilities. From the resulting Boltzmann equation he derived his famous H-theorem, which implies that on average the entropy of an ideal gas can only increase. Unsolved problems in physics: Arrow of time: Why did the universe have such low entropy in the past, resulting in the distinction between past and future and the second law of thermodynamics? Entropy is the only quantity in the physical sciences that picks a particular direction for time, sometimes called... T-symmetry is the symmetry of physical laws under a time-reversal transformation— The universe is not symmetric under time reversal, although in restricted contexts one may find this symmetry. ... Ludwig Boltzmann Ludwig Boltzmann (February 20, 1844 – September 5, Austrian physicist famous for the invention of statistical mechanics. ... In thermodynamics, the H-theorem describes the increase of entropy of an ideal gas in an irreversible process, solving the Boltzmann equation. ... Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of zero volume, with no intermolecular forces. ... In kinetic theory in physics, molecular chaos is the assumption that the velocities of colliding particles are uncorrelated, and independent of position. ... The Boltzmann equation describes the statistical distribution of particles in a fluid. ... In thermodynamics, the H-theorem describes the increase of entropy of an ideal gas in an irreversible process, solving the Boltzmann equation. ...

The assumption of molecular chaos in fact violates time reversal symmetry. It assumes that particle momenta are uncorrelated before collisions. If you replace this assumption with "anti-molecular chaos," namely that particle momenta are uncorrelated after collision, then you can derive an anti-Boltzmann equation and an anti-H-Theorem which implies entropy decreases on average. Thus we see that in reality Boltzmann did not succeed in solving Loschmidt's paradox. The molecular chaos assumption is the key element that introduces the arrow of time. Loschmidts paradox states that if there is a motion of a system that leads to a steady decrease of H (increase of entropy) with time, then there is certainly another allowed state of motion of the system, found by time reversal, in which H must increase. ... This article or section does not cite its references or sources. ...

Applications to living systems

Main article: Entropy and life

The second law of thermodynamics has been proven mathematically for thermodynamic systems, where entropy is defined in terms of heat divided by the absolute temperature. The second law is often applied to other situations, such as the complexity of life, or orderliness.^[6] Some, however, object to this application, on possibly philosophical or theological grounds, reasoning that thermodynamics does not apply to the process of life. In sciences such as biology and biochemistry, however, the application of thermodynamics is well-established, e.g. biological thermodynamics. The general viewpoint on this subject is summarized well by biological thermodynamicist Donald Haynie; as he states: "Any theory claiming to describe how organisms originate and continue to exist by natural causes must be compatible with the first and second laws of thermodynamics."^[7] Over the last century, much writing and research has been devoted to the relationship between the thermodynamic quantity entropy and the evolution of life. ... In physics, heat, symbolized by Q, is defined as transfer of thermal energy [1] Generally, heat is a form of energy transfer associated with the different motions of atoms, molecules and other particles that comprise matter when it is hot and when it is cold. ... Absolute zero is the lowest temperature that can be obtained in any macroscopic system. ... For other uses, see Life (disambiguation). ... Philosophy (from the Greek words philos and sophia meaning love of wisdom) is understood in different ways historically and by different philosophers. ... Theology is literally rational discourse concerning God (Greek θεος, theos, God, + λογος, logos, rational discourse). By extension, it also refers to the study of other religious topics. ... This article or section does not cite any references or sources. ... Biochemistry is the study of the chemical processes and transformations in living organisms. ... Biological thermodynamics (Greek: bios = life and logikos = reason + Greek: thermos = heat and dynamics = power) is the study of energy transformation in the biological sciences. ...

Small systems

In statistical thermodynamics, which uses probability theory to calculated thermodynamic variables, such as entropy, the second law only holds for ensemble averages and the probability for single systems to violate it increases with decreasing size. The fluctuation theorem describes this behaviour. Statistical mechanics is the application of statistics, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... Probability theory is a branch of mathematics concerned with analysis of random phenomena. ... In thermodynamics, state variables, state parameters or thermodynamic variables describe the momentary condition of a system. ... In statistical mechanics, the ensemble average is defined as the weighted average of a molecular property of a system, over the set of states available to the system. ... The second law of thermodynamics stands in apparent contradiction with the time reversible equations of motion for classical and quantum systems. ...

Complex systems

It is occasionally claimed that the second law is incompatible with autonomous self-organisation, or even the coming into existence of complex systems. The entry self-organisation explains how this claim is a misconception. Self-organization refers to a process in which the internal organization of a system, normally an open system, increases automatically without being guided or managed by an outside source. ... Self-organization refers to a process in which the internal organization of a system, normally an open system, increases automatically without being guided or managed by an outside source. ...

In fact, as hot systems cool down in accordance with the second law, it is not unusual for them to undergo spontaneous symmetry breaking, i.e. for structure to spontaneously appear as the temperature drops below a critical threshold. Complex structures, such as Bénard cells, also spontaneously appear where there is a steady flow of energy from a high temperature input source to a low temperature external sink. It is conjectured that such systems tend to evolve into complex, structured, critically unstable "edge of chaos" arrangements, which very nearly maximise the rate of energy degradation (the rate of entropy production).^[8] Spontaneous symmetry breaking in physics takes place when a system that is symmetric with respect to some symmetry group goes into a vacuum state that is not symmetric. ... Bénard cells are obtained in a simple experiment that Bénard, a French physicist, conducted in 1900. ... The phrase edge of chaos was coined by computer scientist Christopher Langton in 1990. ...

Quotes

Wikiquote has a collection of quotations related to:

Second law of thermodynamics

--Sir Arthur Stanley Eddington, The Nature of the Physical World (1927)

--Greg Hill and Kerry Thornley, Principia Discordia (1965)

--Philosopher / Physicist P.W. Bridgman, (1941)

Image File history File links This is a lossless scalable vector image. ... Wikiquote is a sister project of Wikipedia, using the same MediaWiki software. ... The Laws of Nature are claimed in the United States Declaration of Independence to be the work of the Creator of unalienable rights identified as Natures God. ... The Universe is defined as the summation of all particles and energy that exist and the space-time in which all events occur. ... In electromagnetism, Maxwells equations are a set of equations first presented as a distinct group in the later half of the nineteenth century by James Clerk Maxwell. ... One of Sir Arthur Stanley Eddingtons papers announced Einsteins theory of general relativity to the English-speaking world. ... Greg Hill (a. ... Kerry Thornley Kerry Wendell Thornley (April 17, 1938 - November 28, 1998) is perhaps best-known as the co-founder (along with childhood friend Greg Hill) of Discordianism. ... The Loompanics Yellow Cover combined 4th & 5th Edition Principia Discordia, (1979). ... Percy Williams Bridgman (April 21, 1882–August 20, 1961) was an American physicist who won the 1946 Nobel Prize in Physics for his work on the physics of high pressures. ...

Miscellany

• Flanders and Swann produced a setting of a statement of the Second Law of Thermodynamics to music, called "First and Second Law".
• The economist Nicholas Georgescu-Roegen showed the significance of the Entropy Law in the field of economics (see his work The Entropy Law and the Economic Process (1971), Harvard University Press).

Michael Flanders Donald Swann The British duo Flanders and Swann were the actor and singer Michael Flanders (1922–1975) and the composer, pianist and linguist Donald Swann (1923–1994) who collaborated in writing comic songs. ... Categories: Possible copyright violations ...

See also

• Second-law efficiency

Ice melting - classic example of entropy increasing[1] described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice. ... Unsolved problems in physics: Arrow of time: Why did the universe have such low entropy in the past, resulting in the distinction between past and future and the second law of thermodynamics? Entropy is the only quantity in the physical sciences that picks a particular direction for time, sometimes called... The final anthropic principle (FAP) is defined by physicists John D. Barrow and Frank J. Tiplers 1986 book The Anthropic Cosmological Principle as a generalization of the anthropic principle as follows: Final anthropic principle (FAP): Intelligent information-processing must come into existence in the Universe, and, once it comes... The first law of thermodynamics, a generalized expression of the law of the conservation of energy, states: // Description Essentially, the First Law of Thermodynamics declares that energy is conserved for a closed system, with heat and work being the forms of energy transfer. ... Savery Engine [1698] The history of thermodynamics is a core strand in the history of physics and an important one in the history of science. ... The Jarzynski equality (JE) is an equation in statistical mechanics that relates free energy differences between two equilibrium states and non-equilibrium processes. ... The laws of thermodynamics, in principle, describe the specifics for the transport of heat and work in thermodynamic processes. ... Loschmidts paradox states that if there is a motion of a system that leads to a steady decrease of H (increase of entropy) with time, then there is certainly another allowed state of motion of the system, found by time reversal, in which H must increase. ... In physics the Maximum entropy school of thermodynamics (or more colloquially, the MaxEnt school of thermodynamics), initiated with two papers published in the Physical Review by Edwin T. Jaynes in 1957, views statistical mechanics as an inference process: a specific application of inference techniques rooted in information theory, which relate... Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... This article or section should include material from Parallel Path See also Perpetuum mobile as a musical term Perpetual motion machines (the Latin term perpetuum mobile is not uncommon) are a class of hypothetical machines which would produce useful energy in a way science cannot explain (yet). ... Exergy efficiency is also called second-law efficiency because it computes the efficiency of a process taking the second law of thermodynamics into account. ...

References

1. ^ Landau, L.D.; Lifshitz, E.M. (1996). Statistical Physics Part 1. Butterworth Heinemann. ISBN 0-7506-3372-7. 
2. ^ Mendoza, E. (1988). Reflections on the Motive Power of Fire – and other Papers on the Second Law of Thermodynamics by E. Clapeyron and R. Clausius. New York: Dover Publications. ISBN 0-486-44641-7. 
3. ^ Gemmer, Jochen; Alexander Otte & Günter Mahler (2001), "Quantum Approach to a Derivation of the Second Law of Thermodynamics", Phys. Rev. Lett. 86 (10): 1927–1930
4. ^ Stoner, C.D. (2000). Inquiries into the Nature of Free Energy and Entropy - in Biochemical Thermodynamics. Entropy, Vol 2.
5. ^ ^{a b} Clausius, R. (1865). "Mechanical Theory of Heat - with its Application to the Steam Engine and the Physical Properties of Bodies." London: John van Voorst.
6. ^ Hammes, Gordon, G. (2000). Thermodynamics and Kinetics for the Biological Sciences. New York: John Wiley & Sons. ISBN 0-471-37491-1. 
7. ^ Haynie, Donald, T. (2001). Biological Thermodynamics. Cambridge: Cambridge University Press. ISBN 0-521-79549-4. 
8. ^ Kauffman, Stuart (1995). At Home in the Universe - the Search for the Laws of Self-Organization and Complexity. Oxford University Press. ISBN 0-19-509599-5. 

•  Fermi, Enrico [1936] (1956). Thermodynamics. New York: Dover Publications, Inc. ISBN 0-486-60361-X. 

Further reading

• Goldstein, Martin, and Inge F., 1993. The Refrigerator and the Universe. Harvard Univ. Press. A gentle introduction, a bit less technical than this entry.
• Maxwell's demon 2 : entropy, classical and quantum information, computing. Edited by Harvey S. Leff and Andrew F. Rex. Bristol; Philadelphia : Institute of Physics, 2003

External links

• 110+ Variations of the 2nd Law.
• Mechanical Theory of Heat – Nine Memoirs by Rudolf Clausius [1850-1865] on the 1st and 2nd Laws of Thermodynamics.
• Stanford Encyclopedia of Philosophy: "Philosophy of Statistical Mechanics." by Lawrence Sklar.
• The evolution of Carnot's principle, by E.T. Jaynes, in G. J. Erickson and C. R. Smith (eds.) Maximum-Entropy and Bayesian Methods in Science and Engineering vol. 1, p. 267 (1988).
• The Second Law of Thermodynamics.