Predictability refers to the degree that a correct prediction of a system's state can be made either qualitatively or quantitatively. While the second law of thermodynamics can tell us about the equilibrium state that a system will evolve to, and steady states in dissipative systems can sometimes be predicted, there exists no general rule to predict the time evolution of systems far from equilibrium, etc. chaotic systems, if they do not approach some kind of equilibrium. Their predictability usually deteriorates with time. To quantify predictability, the rate of divergence of system trajectories in phase space can be measured (Kolmogorov entropy, Lyapunov exponents). A prediction or forecast is a statement or claim that a particular event will occur in the future. ... A system is an assemblage of inter-related elements comprising a unified whole. ... In physics, the term state is used in several related senses, each of which expresses something about the way a physical system is. ... The second law of thermodynamics, in a concise form, states that the total entropy of any thermodynamically isolated system tends to increase over time, approaching a maximum value. // General description In a general sense, the second law says that the differences between systems in contact with each other tend to... (LTE is an acronym for the progressive-instrumental rock band Liquid Tension Experiment) In thermodynamics, a thermodynamic system is in thermodynamic equilibrium if its energy distribution equals a Maxwell-Boltzmann distribution. ... For alternative meanings see steady state (disambiguation). ... A dissipative system (or dissipative structure) is an open system which is operating far from thermodynamic equilibrium within an environment that exchanges energy, matter or entropy. ... A watch Attempting to understand time has long been a prime occupation for philosophers, scientists and artists. ... Chaos theory, in mathematics and physics, deals with the behaviour of certain nonlinear dynamical systems that (under certain conditions) exhibit the phenomenon known as chaos, most famously characterised by sensitivity to initial conditions (see butterfly effect). ... A trajectory is an imagined trace of positions followed by an object moving through space. ... Phase space is a useful construct in mathematics and physics to demonstrate and visualise the changes in the dynamical variables of a system. ... The Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a measure that characterizes rate of separation of infinitesimaly close trajectories. ...
Whether or not they are unpredictable in terms of computability theory, i.e.,given initial conditions exactly can the result be predicted, seems to be a subject of current research.
Unpredictability is required in some applications, such as the many uses of random numbers in cryptography.
"Unpredictable" random numbers were first investigated in the context of gambling, and many randomizing devices such as dice, shuffling playing cards, and roulette wheels, were first developed for use in gambling.
Clausewitz ought to display a deep and abiding concern for unpredictability and complexity, and consequently to search for ways to express the importance of such matters as context, interaction, effects disproportionate to their causes, sensitivity to initial conditions, time-dependent evolutionary processes, and the serious limitations of linear analysis.
This is a root explanation for unpredictability in those nonlinear phenomena that exhibit chaotic regimes of behavior.
Unpredictability in war due to this second form of chance is thus unavoidable.