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 identi
ties 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 known
results—the excess nonequilibrium Gibbs identity, the path-space irreversibility identity, the
Shiraishi–Funo–Saito speed-dissipation bound, and the KL Pythagorean projection—into a uni
fied work decomposition and efficiency ceiling, all referenced to a common NPT equilibrium base
line. We identify and correct an error that affects a common implementation of the dissipation
rate: the standard formula 12 i̸=j Jij ln(Rijpi/Rjipj) requires the current Jij = Rijpi − Rjipj
as the prefactor, not the one-sided flux Rijpi; using the one-sided flux introduces an O(1) sys
tematic bias that does not vanish with step size. With the correct formula, we validate the
decomposition and bound by integrating the master equation exactly for a three-state NPT
model under linear-ramp protocols across a factor-of-512 sweep in ramp time τ. The residual
between simulated work and the predicted sum ∆Geq +kBT DKL +D is a flat 2.7×10−5 kBT
across the entire sweep—pure discretisation error, confirmed by a convergence test that shows
halving with each doubling of step count—and the SFS inequality is satisfied everywhere.