Counterfactual Entropy Resistance as a Necessary Thermodynamic Condition for Active Living States

We propose a necessary thermodynamic condition for active living states: sustained counterfactual resistance to entropy growth on a pre-registered system boundary and observable manifold. Let H(t) be the coarse-grained Shannon entropy, in bits, of operationally specified observables. The corrected resistance rate is R_res(t) = (dH/dt)_passive − (dH/dt)_actual. The earlier raw rate R_raw(t) = −dH/dt is retained as a useful special case for growth, repair, recovery, ordering, and error-correction episodes, but it is not a general criterion for life: homeostatic non-equilibrium steady states normally have dH/dt ≈ 0 while remaining actively maintained. Under Markovian dynamics with local detailed balance, the entropy balance gives dH/dt = Π_H + J_H, where Π_H ≥ 0 is internal entropy production and J_H is entropy flux into the system, both in bits per unit time. For finite-time raw entropy reduction, the minimum work cost is ⟨W⟩ ≥ Δ⟨E⟩ + k_B T ln2 ∫ R_raw(t) dt = ΔF_neq, with F_neq = ⟨E⟩ − k_B T ln2 · H. Passive detailed-balance relaxation monotonically decreases the relative entropy D(p_t‖p_eq) and the non-equilibrium free energy; Shannon entropy itself is not generally monotonic. This is why the life-relevant condition must be counterfactual rather than raw. Beneath this macroscopic criterion we supply a certified mechanism. In a bipartite split of an active system into a regulated subsystem and its controller, the stochastic thermodynamics of continuous information flow makes sustained negative apparent entropy production, σ_app_X = Π_X + İ_X < 0, a necessary signature of active ordering — bounded below by the information flow the controller supplies and unattainable for a passive, uncontrolled reference. A minimal autonomous model realises this signature at a genuine non-equilibrium steady state, holding the regulated subsystem ordered while total entropy production remains strictly positive. The framework is description-relative, falsifiable, and intended as a Level-1 necessary condition rather than a complete definition of life. Computational examples are interpreted as schematic consistency checks and negative controls, not empirical validation. Direct measurement of R_res(t) in biological systems remains an open experimental task.