Structural Non-Isothermal Equilibrium Induced by Boundary Filtering of Accessible States — A Theoretical Framework Motivated by the Izumi Effect

This manuscript presents a theoretical framework for boundary-induced non-isothermalequilibrium states in dilute gases, motivated by what is referred to as the Izumi effect.In such systems, spatially structured energy distributions emerge and persist in steadystates without macroscopic heat flow or external driving. The central mechanism is boundary filtering of accessible microscopic states.Energy exchange at confining walls selectively samples particle states throughadsorption and re-emission processes, leading to effective spatial variations inenergy distributions even when wall temperatures are identical. The analysis is based on kinetic considerations and statistical state counting,emphasizing how structural constraints at boundaries modify relaxation pathways.The resulting non-isothermal equilibrium does not violate energy conservation ormicroscopic reversibility, but lies outside the domain of validity of the zeroth lawof thermodynamics. This work aims to clarify the physical origin of structurally stabilized temperaturenon-uniformity and to delineate the conditions under which conventional equilibriumassumptions fail. Relation to journal submission:This preprint corresponds to a manuscript currently under editorial consideration at theJournal of Statistical Physics.The content may be revised in response to the peer-review process. Version note:This is Version 1 of the preprint.Future versions may incorporate revisions based on peer-review feedback or additionalanalysis. .