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We introduce the PRISM interstellar medium (ISM) model for thermochemistryand its implementation in the RAMSES-RTZ code. The model includes anon-equilibrium primordial, metal, and molecular chemistry network for 115species coupled to on-the-fly multifrequency radiation transport. PRISMaccurately accounts for the dominant ISM cooling and heating processes in thelow-density regime (i.e. $\rho<10^5\ {\rm cm^{-3}}$), including photoheating,photoelectric heating, H$_2$ heating/cooling, cosmic-ray heating, H/He cooling,metal-line cooling, CO cooling, and dust cooling (recombination and gas-graincollisions). We validate the model by comparing 1D equilibrium simulationsacross six dex in metallicity to existing 1D ISM models in the literature. Weapply PRISM to high-resolution (4.5 pc) isolated dwarf galaxy simulations thatinclude state-of-the-art models for star formation and stellar feedback to takean inventory of which cooling and heating processes dominate each different gasphase of a galaxy and to understand the importance of non-equilibrium effects.We show that most of the ISM gas is either close to thermal equilibrium orexhibits a slight cooling instability, while from a chemical perspective, thenon-equilibrium electron fraction is often more than three times higher orlower than the equilibrium value, which impacts cooling, heating, andobservable emission lines. Electron enhancements are attributed torecombination lags while deficits are shown to be due to rapid cosmic-rayheating. The PRISM model and its coupling to RAMSES-RTZ is applicable to a widevariety of astrophysical scenarios, from cosmological simulations to isolatedgiant molecular clouds, and is particularly useful for understanding howchanges to ISM physics impact observable quantities such as metallic emissionlines.

PRISM: A Non-Equilibrium, Multiphase Interstellar Medium Model for Radiation Hydrodynamics Simulations of Galaxies