Mass as an Operational Entropic Constraint in Quantum Reset and Hawking Emission

This research establishes an operational lower bound on entropy production induced by mass gaps in quantum systems. Using completely positive trace-preserving (CPTP) dynamics, the study demonstrates that any physical reset of a system with a minimal spectral gap \delta_{min}=mc^{2} incurs a minimum entropy production defined by the relation \Sigma\ge mc^{2}/T. Unlike Landauer's principle, this bound follows purely from thermodynamic admissibility and spectral structure rather than logical irreversibility or information-theoretic arguments. Key Features of the Study: ELQR Framework: The research utilizes the Entropy-Limited Quantum Reset (ELQR) framework to model reset as a constrained CPTP control problem. Reinforcement Learning Validation: Optimization using RL agents (specifically PPO) shows that the theoretical bound emerges as a robust dynamical attractor under unconstrained control optimization. Hawking Emission Application: When applied to black-hole horizons, the bound implies a minimal entropic cost for Hawking emission per particle of mass m that is independent of information loss or Page-curve considerations. Many-Body Systems: Validated through tensor-network simulations (TeNPy) of short Heisenberg chains, confirming that the operational bound is robust even in correlated systems. Non-Markovian Extensions: Preliminary simulations of qubits coupled to memory show that while transient backflow occurs, the envelope remains consistent with the mass-induced limit.