Stochastic equations for thermodynamics

Abstract

The applicability of stochastic differential equations to thermodynamics is considered and a new form, different from the classical Itô 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 generalised alternative is proposed. Both expressions coincide in the small-fluctuation limit, providing a normal distribution density.