A Unified Irreversibility Law from Information-Flow Geometry

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“A Unified Irreversibility Law from Information-Flow Geometry.”
The work introduces and proves a universal dynamical law governing coherence loss in open quantum systems, expressed as:

κ˙  =  Φinfo  −  ΔS,\dot{\kappa} \;=\; \Phi_{\mathrm{info}} \;-\; \Delta S ,κ˙=Φinfo−ΔS,

where κ is a convex coherence monotone (Rényi-2 purity-gap), Φ₍info₎ is an information-flux derived from relative entropy to a MaxEnt reference state, and ΔS is Spohn’s entropy production rate. We prove that this decomposition is unique: no other scalar term is permitted under CPTP monotonicity and convexity constraints. This establishes a fundamental “Continuity–Competition Principle” for quantum irreversibility.

We provide quantitative predictions for superconducting qubits, trapped ions, NV centers, and cold-atom platforms, including decoherence-rate suppression, purity pulses, and critical slowing down when information flux balances entropy influx. This package is intended for reproducibility, peer review, and public archiving of the theory, figures, and numerical tools associated with the paper.

Keywords:
quantum thermodynamics, entropy production, coherence dynamics, information geometry, Lindblad dynamics, Spohn theorem, quantum feedback, nonequilibrium physics, quantum information theory, irreversibility, fluctuation theorems