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

We propose entropy resistance as a necessary thermodynamic condition for active living states. The central quantity is counterfactual entropy resistance, Rᵣes (t) = dHₚassive/dt − dHₐctual/dt, defined on a pre-registered system boundary and observable manifold. A system satisfies the Level 1 condition for active organization when it persistently suppresses the entropy growth that would occur under passive dynamics. The earlier raw entropy-reduction rate, Rᵣaw (t) = −dHₛys/dt, is retained only as a special case for growth, repair, recovery, ordering, and error-correction episodes; it is not treated as a general criterion for life, because homeostatic non-equilibrium steady states may have dHₛys/dt ≈ 0 while remaining actively maintained. The framework separates information entropy H, measured in bits, from thermodynamic entropy Sₜh = kB ln (2) H. For finite-time raw entropy reduction, the minimum work cost is ⟨W⟩ ≥ Δ⟨E⟩ + kB T ln (2) ∫₀^τ Rᵣaw (t) dt = ΔFₙeq. Passive detailed-balance relaxation monotonically decreases relative entropy to equilibrium and non-equilibrium free energy, but Shannon entropy itself is not generally monotonic; this motivates the counterfactual rather than raw-entropy formulation. The criterion is substrate-agnostic, scale-agnostic, falsifiable, and explicitly description-relative. It is a necessary condition, not a sufficient definition of life. Computational examples are presented as schematic demonstrations and negative controls, not empirical validation. The framework is intended to complement existing biochemical, evolutionary, and astrobiological definitions by isolating the thermodynamic signature of active organization.