Nonlinear Stochastic Dynamics of Complex Systems, III: Noneqilibrium Thermodynamics of Self-Replication Kinetics

TL;DR

This paper reviews a Markov process-based thermodynamics framework for nonlinear driven mesoscopic systems, applies it to autocatalytic reaction kinetics in nonequilibrium environments, and discusses implications for biochemical self-replication and emergent dissipation.

Contribution

It introduces a general thermodynamic theory for nonlinear stochastic systems and applies it to autocatalytic reactions, highlighting thermodynamic consistency and implications for biological self-replication.

Findings

The theory aligns with classical thermodynamics in equilibrium cases.

Applied to autocatalytic reactions, it models biochemical self-replication.

Discusses the concept of dissipation in biological systems.

Abstract

We briefly review the recently developed, Markov process based isothermal chemical thermodynamics for nonlinear, driven mesoscopic kinetic systems. Both the instantaneous Shannon entropy {\boldmath $S[p_{\alpha}(t)]$} and relative entropy {\boldmath $F[p_{\alpha}(t)]$}, defined based on probability distribution {\boldmath $\{p_{\alpha}(t)\}$}, play prominent roles. The theory is general; and as a special case when a chemical reaction system is situated in an equilibrium environment, it agrees perfectly with Gibbsian chemical thermodynamics: {\boldmath $k_BS$} and {\boldmath $k_BTF$} become thermodynamic entropy and free energy, respectively. We apply this theory to a fully reversible autocatalytic reaction kinetics, represented by a Delbr\"{u}ck-Gillespie process, in a chemostatic nonequilibrium environment. The open, driven chemical system serves as an archetype for biochemical self-replication. The significance of {\em thermodynamically consistent} kinetic coarse-graining is emphasized. In a kinetic system where death of a biological organism is treated as the reversal of its birth, the meaning of mathematically emergent "dissipation", which is not related to the heat measured in terms of {\boldmath $k_BT$}, remains to be further investigated.