Fluctuations and non-equilibrium thermodynamics

A closed macroscopic system with fluctuating local properties is treated as a thermodynamic system with internal degrees of freedom. Gibb’s entropy postulate is used to define the systems’ entropy as a functional of the probability density in internal coordinate space. It is shown that application of the scheme of thermodynamics of irreversible processes then leads directly to the theory of fluctuations as Markov processes described by a multivariate Fokker–Planck equation. In this perspective fluctuation theory may be said to have become integrated into non-equilibrium thermodynamics.