A Unified Irreversibility Law from Information-Flow Geometry

Kelly Rhys

Published Dec 27, 2025• 0 citations

Abstract

This work introduces a unified dynamical law of irreversibility that links three fundamental quantities in open quantum systems: coherence change, information flux, and irreversible entropy production.For finite-dimensional systems evolving under completely positive trace-preserving (CPTP) Markovian semigroups, we prove the exact identity κ˙(t)=Φinfo(t)−ΔS(t),\dot{\kappa}(t) = \Phi_{\text{info}}(t) - \Delta S(t),κ˙(t)=Φinfo(t)−ΔS(t), where κ(t)=S(ρdiag)−S(ρ)\kappa(t) = S(\rho_{\text{diag}}) - S(\rho)κ(t)=S(ρdiag)−S(ρ) is the entropy-valued coherence, Φinfo(t)=−ddtS(ρt∥ν)\Phi_{\text{info}}(t) = -\frac{d}{dt} S(\rho_t \Vert \nu)Φinfo(t)=−dtdS(ρt∥ν) is the information flux relative to a canonical maximum-entropy reference state ν\nuν, and ΔS(t)=Tr[L(ρt)(log⁡ρt−log⁡σ)]≥0\Delta S(t) = \text{Tr}[ \mathcal{L}(\rho_t)(\log \rho_t - \log \sigma)] \ge 0ΔS(t)=Tr[L(ρt)(logρt−logσ)]≥0 is the Spohn entropy production rate. The result establishes an exact entropy-balance identity connecting quantum coherence, thermodynamic irreversibility, and information flow — all expressed in consistent entropy-per-time units.Operational protocols are provided for experimental validation using modern quantum platforms (e.g., superconducting qubits, trapped ions, or cavity QED).A residual test, R(t)=κ˙−Φinfo+ΔSR(t) = \dot{\kappa} - \Phi_{\text{info}} + \Delta SR(t)=κ˙−Φinfo+ΔS, offers a falsifiable criterion for detecting non-Markovianity or hidden memory flux. The framework unifies information geometry, resource-theoretic coherence, and nonequilibrium thermodynamics into a single experimentally testable law, illuminating how quantum structure can be sustained only when information inflow compensates entropy production. Keywords:Quantum thermodynamics, information theory, open quantum systems, coherence, entropy production, relative entropy, Lindblad dynamics, irreversibility, information geometry.

DOI: 10.5281/zenodo.18071407

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