In thermodynamics, specifically in statistical mechanics, the Gibbs entropy is the usual statistical mechanical entropy of a thermodynamic system, Thermodynamics (from the Greek thermos meaning heat and dynamis meaning power) is a branch of physics that studies the effects of temperature, pressure, and volume changes on physical systems at the macroscopic scale. ... 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. ...

where the summation is taken over the possible states of the system as a whole (typically a 6N-dimensional space, if the system contains N separate particles).

The importance of this formula is discussed at much greater length in the main article Entropy (thermodynamics). In thermodynamics and statistical mechanics, the thermodynamic entropy (or simply the entropy) S is a key physical variable in describing a thermodynamic system. ...

Often, according to context, S is just called the statistical entropy, or the thermodynamic entropy, or simply the entropy. However the term Gibbs entropy can be useful to distinguish it from the earlier Boltzmann entropy, which neglected internal statistical correlations in the overall particle distribution.

See also

• J. Willard Gibbs

Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American physical chemist. ...

References

• Jaynes, E. T. (1965). Gibbs vs Boltzmann entropies. American Journal of Physics, 33, 391-8.