Intrinsic and Extrinsic Thermodynamics for Stochastic Population Processes with Multi-Level Large-Deviation Structure.

Eric Smith

doi:10.3390/e22101137

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 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 that is known to exist, into a relative entropy and a housekeeping entropy rate, is taken here to define respectively the intensive thermodynamics of a system and an 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 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.

Highlights

The statistical derivations underlying most thermodynamic phenomena are understood to be widely applicable, and are mostly developed in general terms
Where thermodynamics is offered as an ontology to understand new patterns and causes in nature—the thermodynamics of computation [1,2,3,4] or stochastic thermodynamics [5], or where these methods are taken to define a foundation for the statistical physics of reproduction or adaptation [6,7]—these problems are framed in terms of two properties particular to the domain of mechanics: the conservation of energy and microscopic reversibility
Active today, stochastic thermodynamics is the modern realization of a program to create a non-equilibrium thermodynamics that began with Onsager [11,12] and took much of its modern form under Prigogine and coworkers [13,14]

Summary

Introduction

The statistical derivations underlying most thermodynamic phenomena are understood to be widely applicable, and are mostly developed in general terms. Stochastic thermodynamics combined elements of both traditions, with the quantities termed “non-equilibrium entropies” corresponding to the information entropies over computer states, distinct from quasistatic entropies associated with heat in a locally-equilibrium environment, with boundary conditions altered by the explicitly-modeled stochastic state transitions. Stochastic thermodynamics incorporated time-reversal methods originally developed for measures in dynamical systems [15,16,17,18] leading to a variety of fluctuation theorems [19,20,21] and non-equilibrium work relations [22,23,24], still, relating path probability ratios either to dissipation of heat or to differences in equilibrium free energies

Results

Discussion

Conclusion