Reconstructing Temperature from Escape Dynamics in Constrained Systems

Temperature is a central concept in statistical physics, yet its operational meaning is typically tied to equilibrium ensembles or thermodynamic relations. Here we propose an alternative formulation within Energy-Efficiency Theory (EET) in which temperature is reconstructed from the escape dynamics of constrained-state energy. We define an escape tendency λ as the measurable rate of barrier-crossing events in a constrained system, without assuming prior knowledge of temperature. Empirically, escape rates in many systems exhibit an approximately exponential dependence on barrier energy. We interpret this scaling as defining temperature as a parameter reconstructed from escape statistics, rather than a primitive quantity. This formulation provides a unified dynamical perspective connecting thermal activation, quantum tunneling, and radiative emission. It offers an interpretation of temperature applicable across classical, quantum, and gravitational regimes, while remaining consistent with established statistical formalisms and forming a natural component of the Energy-Efficiency Theory framework.