Structural Non-Isothermal Equilibrium Induced by Boundary Filtering of Accessible States II — Microprocesses of the Izumi Effect and Thermodynamic Implications

We investigate how boundary microprocesses can select stationary states that are equilibrium-like yet non-isothermal. Motivated by the Izumi effect, we formulate boundary exchange in terms of a collision-conditioned transition kernel and introduce a flux-weighted effective number of accessible states, W₄₅₅ (₄䂲, ₗ), ₖ₈ₓ₇ ₀₍ ₀ₒₒ₎₂₈₀ₓ₄₃ ₄₅₅₄₂ₓ₈ₕ₄ ₄₍ₓₑ₎₏ₘ ₒ_₄₅₅=k ₁ W₄₅₅. In a minimal 1D normal-channel model, the collision weight C (Eₓ) |vₓ| Eₓ^{1/2 cancels the 1D density-of-states factor g₁ ₃ (Eₓ) Eₓ^-1/2, so that the boundary-conditioned exchange spectrum becomes shape-controlled by the wall bosonic occupation with an adsorption shift, f₁₄ (Eₓ+Vw). Starting from a two-wall operator, we derive particle- and energy-flux functionals and show that, when adsorption shifts differ (VA VB), the stationarity constraints for particle flux and energy flux generically do not coincide with the standard grand-canonical fixed point. This mismatch produces robust structural non-isothermal stationarity selected by the boundary kernel class rather than by bulk gradients. We further construct a work-extraction and regeneration cycle based on kernel-class switching (e. g. \ gas exchange) and provide explicit first-law bookkeeping. Finally, we identify which textbook assumptions are bypassed (global ergodicity, equal a priori probability on the full energy shell, and the premises behind H-theorems) while retaining Liouvillean bulk dynamics and microreversibility, and we propose a minimal thermodynamic reinterpretation in which the Zeroth and Second Laws are boundary-conditioned fixed-point statements. }