Thermodynamic contraction of disturbance-rejection capacity in constrained Markov networks

This preprint develops a local thermodynamic characterization of disturbance-rejection capacity in constrained finite-state Markov networks. For a specified family of bounded locally detailed-balanced support channels, it distinguishes the raw kinetic disturbance-rejection set permitted by the available channel activities from the thermodynamically admissible subset remaining under a finite sustaining budget. At a fixed constrained state, disturbances enter the instantaneous viability conditions through their components normal to the active constraint faces. Combining these requirements with channel-resolved entropy-production costs yields an exact thermodynamic contraction of the raw kinetic set. The directional loss of kinetic authority is quantified by a support-function maneuverability deficit. For independently supported active faces, the admissible set is the intersection of individual channel-saturation bounds with a weighted-simplex thermodynamic constraint. Its directional coefficients are the entropy-production cost per unit inward normal effectiveness of the specified physical transition channels, rather than externally chosen control penalties. A finite-activity specialization further shows that approaching reversible support cannot drive this thermodynamic price to zero while maintaining finite kinetic authority. A solvable three-state Markov model separates thermodynamic contraction from support-architecture effects. Independent and shared gating can have the same maintained distribution, aggregate generator, channel rates, and entropy-production rate at the present operating point while admitting different residual directional disturbance-rejection sets. Thus present maintained observables need not determine future directional rejection capability when the support architecture is not itself specified. The construction is explicitly local and instantaneous. Finite-horizon evolution of resource states, support effectiveness, active geometry, and thermodynamic costs is left to a subsequent trajectory-level treatment.