Conservation laws and symmetries in stochastic thermodynamics

TL;DR

This paper explores how the topology of a system's configuration space influences the fundamental thermodynamic forces and currents in stochastic thermodynamics, linking conservation laws and symmetries to dissipation.

Contribution

It introduces a general algorithm to identify fundamental affinities and currents based on conservation laws and symmetries in stochastic thermodynamics.

Findings

Topology determines the number of independent thermodynamic affinities.

The algorithm identifies fundamental affinities and currents from conservation laws and symmetries.

The framework unifies macroscopic conservation laws with microscopic detailed balance.

Abstract

Phenomenological nonequilibrium thermodynamics describes how fluxes of conserved quantities such as matter, energy and charge flow from outer reservoirs across a system, and how they irreversibly degrade from one form to another. Stochastic thermodynamics is formulated in terms of probability fluxes circulating in the system's configuration space. The consistency of the two frameworks is granted by the condition of local detailed balance, which specifies the amount of physical quantities exchanged with the reservoirs during single transitions between configurations. We demonstrate that the topology of the configuration space crucially determines the number of independent thermodynamic affinities (forces) that the reservoirs generate across the system, and provide a general algorithm that produces the fundamental affinities and their conjugate currents contributing to the total dissipation, based on the interplay between macroscopic conservations laws for the currents and microscopic symmetries of the affinities.