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

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.