Stochastic equations for thermodynamics

TL;DR

This paper introduces a new form of stochastic differential equations tailored for thermodynamics, offering a better description of fluctuations and discussing the validity of the Boltzmann-Einstein principle.

Contribution

A novel stochastic differential equation form for thermodynamics is proposed, improving fluctuation modeling and extending the Boltzmann-Einstein principle's applicability.

Findings

New stochastic form better describes thermodynamic fluctuations

Proposed generalized Boltzmann-Einstein principle

Both forms agree in the small fluctuation limit

Abstract

The applicability of stochastic differential equations to thermodynamics is considered and a new form, different from the classical Ito and Stratonovich forms, is introduced. It is shown that the new presentation is more appropriate for the description of thermodynamic fluctuations. The range of validity of the Boltzmann-Einstein principle is also discussed and a generalized alternative is proposed. Both expressions coincide in the small fluctuation limit, providing a normal distribution density.