Stochastic deformation of a thermodynamic symplectic structure

TL;DR

This paper introduces a stochastic deformation approach to thermodynamic symplectic structures, revealing gauge symmetries and fields that describe fluctuations and are applicable to systems with distributed parameters.

Contribution

It develops a novel stochastic deformation framework for thermodynamics, analogous to deformation quantization, and uncovers gauge symmetries and fields relevant to thermodynamic fluctuations.

Findings

Gauge symmetries of thermodynamics are identified.

Stochastic mechanics describing fluctuations is formulated.

Application to systems with distributed parameters is demonstrated.

Abstract

A stochastic deformation of a thermodynamic symplectic structure is studied. The stochastic deformation procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation parameter (the Planck constant). Gauge symmetries of thermodynamics and corresponding stochastic mechanics, which describes fluctuations of a thermodynamic system, are revealed and gauge fields are introduced. A physical interpretation to the gauge transformations and gauge fields is given. An application of the formalism to a description of systems with distributed parameters in a local thermodynamic equilibrium is considered.