  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 \emph{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 is shown to exist, into a relative
entropy and a housekeeping entropy rate, which define respectively the
\textit{intensive} thermodynamics of a system and an \textit{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 \emph{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.
