Information–Energetic Thermodynamics (IET): Formal Definitions, Irreversible Decisions, and the VIRR Metric

We formulate Information–Energetic Thermodynamics (IET) as an operational framework for quantifying the energetic efficiency of physically stabilized information processing in finite-time systems. In contrast to conventional throughput-based metrics and entropy-production measures, the framework introduces the concept of a physically stabilized irreversible decision event, defined as a transition between metastable attractors satisfying explicit localization, stability, and thermodynamic irreversibility criteria. Within this structure, we define the Valid Irreversible Resolution Rate (VIRR) as the asymptotic rate of such stabilized decision events per unit supplied energy. We show that VIRR is bounded from above by the reversible free-energy difference associated with attractor transitions, ensuring compatibility with the second law of thermodynamics. Using a stochastic bistable system governed by overdamped Langevin dynamics, we analyze finite-time entropy production and demonstrate how dissipation and protocol duration affect the energetic cost per stabilized event. We further prove that the irreversible decision rate is not reducible to entropy production alone by constructing explicit counterexamples in which identical total entropy production yields different stabilized decision rates. This establishes VIRR as a distinct observable within nonequilibrium thermodynamics. The proposed framework provides a physically grounded and experimentally accessible measure of energy-to-information conversion that applies across classical and quantum systems operating far from equilibrium, and enables consistent comparison of heterogeneous information-processing architectures.