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A Unified Irreversibility Law from Information-Flow Geometry

Authors: Rhys, Kelly;

A Unified Irreversibility Law from Information-Flow Geometry

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.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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