The dimensionless energy information time invariant as a universal benchmark for reversibility in quantum and mesoscopic thermodynamics

Article type: Foundational Theory / Methodological Protocol. Landauer's principle establishes that erasing one bit of information requires at least \((k_B T\ln 2)\) of energy, a limit that experiments have approached but never violated [Landauer1961,Berut2012,Jun2014]. As quantum processors, mesoscopic feedback engines and neuromorphic architectures scale up, they operate in regimes where energetic efficiency, reliable information flow and proximity to reversible thermodynamic limits jointly determine performance. Existing descriptors---entropy production, Landauer bounds or power-efficiency measures---capture only isolated aspects of the problem and do not unify (i) energetic throughput, (ii) reliably used information rate and (iii) the reversible per-bit baseline from the same physical process.To address this gap, I introduce the energy--information--time (EIT) invariant:\[\tilde N_t = \frac{P}{\varepsilon_b\,\dot I},\]the first dimensionless, task-normalized metric for energetic reversibility across heterogeneous platforms. Here \((P)\) is incremental protocol power, \((\dot I)\) the reliably processed information rate and \((\varepsilon_b)\) the reversible free-energy baseline per bit. In the Landauer regime \((\varepsilon_b = k_B T\ln 2)\) and reversible operation corresponds to \((\tilde N_t\to 1)\).The contributions of this paper are threefold: (i) a derivation of the invariant from free-energy equalities and information-theoretic relations, showing it encodes operational content not accessible through entropy production alone; (ii) a complete metrological framework for evaluating \((P)\), \((\dot I)\) and \((\varepsilon_b)\), including uncertainty budgets and constant-\((T)\) finite-time scaling diagnostics; and (iii) a laboratory protocol for circuit-QED (cQED) reset/feedback experiments in which the invariant can be directly measured. Published Landauer-erasure and feedback-engine results serve only as external illustrations of near-optimal regimes [Berut2012,Jun2014]; no new primary data are reported. This work therefore provides a unified invariant with a reproducible evaluation procedure designed for future experimental implementation.