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We briefly review the recently developed Markov process-based isothermal chemical thermodynamics for nonlinear driven mesoscopic kinetic systems. Both the instantaneous Shannon entropy <inline-formula> <tex-math notation="LaTeX">$S[\,p_{\alpha }(t)]$ </tex-math></inline-formula> and relative entropy <inline-formula> <tex-math notation="LaTeX">$F[\,p_{\alpha }(t)]$ </tex-math></inline-formula>, defined based on probability distribution <inline-formula> <tex-math notation="LaTeX">$\{\,p_{\alpha }(t);\alpha \in \boldsymbol {\mathscr {S}}\}$ </tex-math></inline-formula> over a state space <inline-formula> <tex-math notation="LaTeX">$\mathscr {S}$ </tex-math></inline-formula>, 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: <inline-formula> <tex-math notation="LaTeX">$k_{B}S$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$k_{B}TF$ </tex-math></inline-formula> become thermodynamic entropy and free energy, respectively. We apply this theory to a fully reversible autocatalytic reaction kinetics, represented by a Delbr&#x00FC;ck&#x2013;Gillespie process, in a chemostatic nonequilibrium environment. The open driven chemical system serves as an archetype for biochemical self-replication and provides insight into a recent theory of England. The significance of <italic>thermodynamically consistent</italic> 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 &#x201C;dissipation,&#x201D; which is not related to the heat measured in terms of <inline-formula> <tex-math notation="LaTeX">$k_{B}T$ </tex-math></inline-formula>, remains to be further investigated.

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