Thermodynamic Allocation of Disturbance-Rejection Capacity in Constrained Markov Networks Use the exact manuscript title.

Finite-state Markov systems maintained away from equilibrium may remain operational only while available driving can oppose outward motion through active constraint boundaries. We characterize the additional disturbances that such a system can reject when restoring dynamics are supplied by bounded locally detailed-balanced transition channels. At a fixed constrained state, a disturbance enters local viability only through its components normal to the active constraint faces. Combining these geometric requirements with channel-resolved entropy production yields an exact thermodynamic disturbance-rejection set. The minimum dissipation required merely to maintain the active boundary equals the retained-nominal-channel contribution underlying the Horowitz–Zhou–England maintenance bound plus a nonnegative support cost fixed by the active geometry and specified support channels, giving a conditional tightening of that nominal floor. For independently supported constraint directions, the remaining rejection capacity obeys an exact weighted-simplex thermodynamic constraint, together with the individual channel-saturation bounds, whose exchange rates are the entropy-production cost per unit inward normal velocity. A three-state Markov model shows that a finite dissipative-power supply couples otherwise independent disturbance directions and that support architecture can further contract the resulting maneuverability set without changing the present maintained state, generator, or entropy-production rate.