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This paper proposes a novel framework called "leaf typicality" to unify the statistical mechanics of equilibrium and nonequilibrium quantum states by minimizing energy variance in pure state ensembles. The study suggests that thermodynamic compression leads to indistinguishability among states with identical energy densities, offering new insights into how stationary states generalize beyond traditional eigenstate thermalization. These findings advance fundamental theoretical understanding rather than addressing immediate hardware or application-level developments.
A Route to Quantum-Coherent Thermodynamics
arXiv:2602.12212v4 Announce Type: replace Abstract: Equilibrium thermodynamics emerges because a vast number of microscopic states become indistinguishable at the level of local observables. We start from the observation that a nonequilibrium quantum state can also be represented by an ensemble of pure states that minimizes the average energy variance. We show that varying the statistical weights within this optimal family organizes state space into ``minimum-variance leaves'', which generalize the space of stationary states underlying equilibrium. We observe thermodynamic compression on the leaves, which in the simplest scenario manifests itself in the indistinguishability of states with the same energy density. We call this ``leaf typicality''; at equilibrium it reduces to eigenstate thermalization or its generalizations. Numerical tests support leaf typicality on some leaves and indicate a breakdown of its stronger forms on others, suggesting a rich thermodynamic organization beyond equilibrium. These results open a route to a unified statistical mechanics of equilibrium and nonequilibrium quantum states.
Abstract:Equilibrium thermodynamics emerges because a vast number of microscopic states become indistinguishable at the level of local observables. We start from the observation that a nonequilibrium quantum state can also be represented by an ensemble of pure states that minimizes the average energy variance. We show that varying the statistical weights within this optimal family organizes state space into ``minimum-variance leaves'', which generalize the space of stationary states underlying equilibrium. We observe thermodynamic compression on the leaves, which in the simplest scenario manifests itself in the indistinguishability of states with the same energy density. We call this ``leaf typicality''; at equilibrium it reduces to eigenstate thermalization or its generalizations. Numerical tests support leaf typicality on some leaves and indicate a breakdown of its stronger forms on others, suggesting a rich thermodynamic organization beyond equilibrium. These results open a route to a unified statistical mechanics of equilibrium and nonequilibrium quantum states.
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph)
arXiv:2602.12212 [quant-ph]
(or arXiv:2602.12212v4 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2602.12212 Focus to learn more arXiv-issued DOI via DataCite
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