Temperature Beyond Equilibrium in Isolated Quantum Many-Body Systems and Their Subsystems

Abstract

Temperature is one of the central concepts of thermodynamics, yet its meaning far from equilibrium remains unclear. The problem is especially challenging in isolated quantum many-body systems, whose states evolve unitarily, may remain far from equilibrium, and retain energy coherence, a genuinely quantum feature with no direct classical counterpart. Specifically, energy fluctuations in a nonstationary quantum state have two distinct origins. Part of them comes from uncertainty in the energy populations and has the usual thermodynamic meaning. The rest comes from quantum coherence between energy sectors and is responsible for the state's time dependence. We propose that, even away from equilibrium, temperature identifies the state within the family of regular states sharing the same energy-coherence structure. This provides a natural definition of temperature for a broad class of nonequilibrium quantum states. The resulting inverse temperature is not, in general, obtained by differentiating entropy with respect to energy. The usual maximum-entropy principle is instead replaced by a principle of minimum discrimination information, which selects the least distinguishable state compatible with the prescribed energy and coherence structure. We also extend the construction to subsystems and show that, although their inverse temperature is not determined by the reduced state alone, its instantaneous rate of change is a local quantity, determined by the thermodynamic structure induced on the subsystem at that time.