Intrinsic and extrinsic thermodynamics for stochastic population processes with multi-level large-deviation structure

TL;DR

This paper develops a thermodynamic framework for stochastic population processes based on large-deviation theory, introducing concepts of macrostate, irreversibility decomposition, and information measures, applicable even without conservation laws.

Contribution

It introduces a novel thermodynamic description for hierarchical stochastic systems using large-deviation properties, independent of microscopic reversibility or conservation laws.

Findings

Decomposition of irreversibility into relative entropy and housekeeping entropy rate.

Legendre duality for housekeeping entropy in irreversible processes.

Application to stochastic Chemical Reaction Networks.

Abstract

A set of core features is set forth as the essence of a thermodynamic description, which derive from large-deviation properties in systems with hierarchies of timescales, but which are \emph{not} dependent upon conservation laws or microscopic reversibility in the substrate hosting the process. The most fundamental elements are the concept of a macrostate in relation to the large-deviation entropy, and the decomposition of contributions to irreversibility among interacting subsystems, which is the origin of the dependence on a concept of heat in both classical and stochastic thermodynamics. A natural decomposition is shown to exist, into a relative entropy and a housekeeping entropy rate, which define respectively the \textit{intensive} thermodynamics of a system and an \textit{extensive} thermodynamic vector embedding the system in its context. Both intensive and extensive components are functions of Hartley information of the momentary system stationary state, which is information \emph{about} the joint effect of system processes on its contribution to irreversibility. Results are derived for stochastic Chemical Reaction Networks, including a Legendre duality for the housekeeping entropy rate to thermodynamically characterize fully-irreversible processes on an equal footing with those at the opposite limit of detailed-balance. The work is meant to encourage development of inherent thermodynamic descriptions for rule-based systems and the living state, which are not conceived as reductive explanations to heat flows.