Non-equilibrium Thermodynamics and Hydrodynamic Fluctuations

TL;DR

This paper reformulates nonequilibrium thermodynamics to incorporate fluctuations, deriving a Fokker-Planck equation that describes the evolution of hydrodynamic fluctuations in a simple fluid, linking thermodynamics and stochastic processes.

Contribution

It introduces a new thermodynamic framework that explicitly accounts for fluctuations and derives the associated Fokker-Planck equation for hydrodynamic behavior.

Findings

Derivation of the Fokker-Planck equation for hydrodynamic fluctuations.

Explicit connection between thermodynamic irreversibility and stochastic dynamics.

Framework applicable to simple fluids for analyzing nonequilibrium fluctuations.

Abstract

The reformulation of nonequilibirum thermodynamics, to include the treatment of thermodynamic fluctuations, is applied to the hydrodynamic fluctuations of a simple fluid. It is shown that the nonequilibrium thermodynamic scheme leads to the explicit form of the Fokker-Planck equation which describes the time behaviour of the probability distribution function of these hydrodynamic fluctuations as well as the irreversible processes which are connected with this behaviour.