The Irreversibility Plane: Response Asymmetry and Dissipation Are Independent Coordinates of Strategic Non-Equilibrium

Distance from equilibrium is treated as a scalar for strategic systems. A local reading, theasymmetry of the equilibrium response to payoff perturbations, and a global reading, theentropy production of the revision dynamics, are used interchangeably because both vanishon potential games. This paper measures whether they carry the same information. Onfamilies of two-player games generated at a prescribed harmonic fraction α of the Candogandecomposition, the two readings co-move almost perfectly across the family (SpearmanρS = 0.9927 [0.9914,0.9936], n= 1000), and that agreement is a confound: each reading isseparately monotone in α (0.9904 and 0.9819). Conditioning on α removes it. Within a levelthe association falls from +0.851 at α= 0.05, at m= 3 and n= 200, to an upper 95% intervalendpoint below 0.35 at every action count tested, m∈{3,4,5,6}, worst +0.156, with thelow-α and high-α intervals disjoint at every m. The two readings share a zero and little else,so an observed system should be located by a point in a plane and not by a number on a line.No system measured here carries both coordinates, so the plane is demonstrated on syntheticfamilies and anchored, not populated, by the two real readings. The structural possibilitythat a local response object and a global dissipation object come apart is not new and is notclaimed here: it is established for Markov jump processes and is exactly false in the Langevinclass, which makes it class-dependent. What is reported is the instantiation of both readingson finite strategic-form games, the harmonic fraction as the computable coordinate alongwhich the breakdown is parameterised, and the measurement. The evidence is two-playerthroughout. At three and four players the low-α coupling that the stratified design needs asa baseline falls below the registered 0.55 precondition (+0.378 and +0.172, against +0.847at N = 2), so the registered player-count kill-shot returns indeterminate instead of a pass,and the finite-size kill-shot returns indeterminate under the registration that binds it. Bothverdicts, a criterion substitution inside the finite-size unit, and a refuted repair are reportedin the body.