STEF - Finiteness of Entropy Production as a Criterion of Physical Admissibility

STEF—Space Time Entropy Finiteness—is presented as a criterion for assessing the physical admissibility of ideal solutions rather than as an alternative cosmological theory. The framework takes the dynamics supplied by established theories as input and asks which candidate solutions can be realized through complete physical processes once nonequilibrium resources, system boundaries, environment, measurement, control, and recording are made explicit. The mathematical core combines Markov’s inequality with an independent physical inclusion relating the operationally defined active domain M_act(P) to a superlevel set of the entropy-production density. The resulting active four-volume bound is conditional: its physical content depends on deriving or measuring a non-degenerate threshold, a minimum entropy cost per time window, a non-degenerate asymptotic mean, or an equivalent non-integrability condition. The paper explicitly examines counterexamples that prevent stronger conclusions from following from the second law alone. Local applications to finite-time thermodynamics, information processing, and thermodynamic computing are proposed as experimentally accessible tests. A possible application to FLRW cosmology is formulated only as a conditional research programme, because convergence of cumulative entropy production depends on matter content, active physical volume, and the asymptotic behaviour of the production density. STEF therefore functions as a reality filter: it becomes a new physical bound only within domains where the required entropic cost is independently established, while global claims about the finiteness of space or time remain conjectural and require additional bridge laws and observational evidence.