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

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 $k_{B}S$} and {\boldmath $k_{B}TF$} become thermodynamic entropy and free energy, respectively. We apply this theory to a fully reversible autocatalytic reaction kinetics, represented by a Delbrück-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 $k_{B}T$}, remains to be further investigated.

10 page

References in corpus (10)

• The large deviation approach to statistical mechanics
• Ensemble and Trajectory Thermodynamics: A Brief Introduction
• Fluctuation Theorem for Arbitrary Open Quantum Systems
• Work and information processing in a solvable model of Maxwell's demon
• Mesoscopic Kinetic Basis of Macroscopic Chemical Thermodynamics: A Mathematical Theory
• Entropy Production in Mesoscopic Stochastic Thermodynamics: Nonequilibrium Kinetic Cycles Driven by Chemical Potentials, Temperatures, and Mechanical Forces
• Nonequilibrium Thermodynamic Formalism of Nonlinear Chemical Reaction Systems with Waage-Guldberg's Law of Mass Action
• Irreversible Thermodynamics in Multiscale Stochastic Dynamical Systems
• Model simplification and loss of irreversibility
• Nonlinear Stochastic Dynamics of Complex Systems, II: Potential of Entropic Force in Markov Systems with Nonequilibrium Steady State, Generalized Gibbs Function and Criticality

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