The Transduction Bound: An Integrated Information-Thermodynamic Theorem for NPT Markov Jump Processes

We present a synthesis of information-thermodynamic identities for thermally open,driven continuous-time Markov jump processes coupled to an isothermal-isobaric (NPT)bath at fixed temperature T and pressure P. By integrating concepts from Renormalization Group Flow and Kuramoto Synchronization, we propose a framework that segmentsthe field into distinct phases: Distillation, Synchronization, and Legacy. Technically, weassemble: (i) an exact state-space identity equating excess nonequilibrium Gibbs potentialwith kBTDKL(p||π); (ii) a path-space identity equating mean entropy production with aKL divergence between forward and time-reversed path measures; (iii) an exact mean workdecomposition into ∆Geq, stored nonequilibrium “charge”, and irreversible dissipation; (iv)a finite-time speed-dissipation constraint (Shiraishi-Funo-Saito) and efficiency ceiling; and(v) an information-geometric Pythagorean (projection) decomposition relative to constraintmanifolds. This “Transduction Bound” serves not only as a rigorous efficiency ceiling butalso as a topological bridge, resolving the “monologue” of static field theories into a “dialogue” of active observers