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 Hₛys (t) be the coarse-grained Shannon entropy, in bits, of operationally specified observables. The corrected resistance rate is Rᵣes (t) ≡ (dHₛys/dt) ₚassive - (dHₛys/dt) ₐctual. The earlier raw rate Rᵣaw (t) = -dHₛys/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 dHₛys/dt ≈ 0 while remaining actively maintained. Under Markovian dynamics with local detailed balance, the entropy balance gives dHₛys/dt = ΠH + JH where ΠH ≥ 0 is internal entropy production and JH 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⟩ + kB T ln (2) ∫₀^τ Rᵣaw (t) dt = ΔFₙeq with Fₙeq = ⟨E⟩ - kB T ln (2) Hₛys. Passive detailed-balance relaxation monotonically decreases the relative entropy D (pₜ || pₑq) 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. 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 Rᵣes (t) in biological systems remains an open experimental task.
Onur Ece (Sun,) studied this question.