A Unit-Consistent NPT Work-Decomposition Protocol for Driven Markov Jump Processes Exact Identities, Finite-Time Bounds, and Numerical Validation

We present a self-contained, unit-consistent synthesis of information-thermodynamic identities for driven continuous-time Markov jump processes coupled to an isothermal-isobaric (NPT)bath. The contribution is a single numerically auditable protocol that assembles four knownresults—the excess nonequilibrium Gibbs identity, the path-space irreversibility identity, theShiraishi–Funo–Saito speed-dissipation bound, and the KL Pythagorean projection—into a unified work decomposition and efficiency ceiling, all referenced to a common NPT equilibrium baseline. We identify and correct an error that affects a common implementation of the dissipationrate: the standard formula 12 i̸=j Jij ln(Rijpi/Rjipj) requires the current Jij = Rijpi − Rjipjas the prefactor, not the one-sided flux Rijpi; using the one-sided flux introduces an O(1) systematic bias that does not vanish with step size. With the correct formula, we validate thedecomposition and bound by integrating the master equation exactly for a three-state NPTmodel under linear-ramp protocols across a factor-of-512 sweep in ramp time τ. The residualbetween simulated work and the predicted sum ∆Geq +kBT DKL +D is a flat 2.7×10−5 kBTacross the entire sweep—pure discretisation error, confirmed by a convergence test that showshalving with each doubling of step count—and the SFS inequality is satisfied everywhere.