Strong Coupling and non-Markovian Effects in the Statistical Notion of Temperature

Abstract

We investigate the emergence of temperature $T$ in the system-plus-reservoir paradigm starting from the fundamental microcanonical scenario at total fixed energy $E$ where, contrary to the canonical approach, $T=T(E)$ is not a control parameter but a derived auxiliary concept. As shown by Schwinger for the regime of weak coupling $\gamma$ between subsystems, $T(E)$ emerges from the saddle-point analysis leading to the ensemble equivalence up to corrections $\mathcal{O}(1/\sqrt{N})$ in the number of particles $N$ that defines the thermodynamic limit. By extending these ideas for finite $\gamma$, while keeping $N\to \infty$, we provide a consistent generalization of temperature $T(E,\gamma )$ in strongly coupled systems and we illustrate its main features for the specific model of Quantum Brownian Motion where it leads to consistent microcanonical thermodynamics. Interestingly, while this $T(E,\gamma )$ is a monotonically increasing function of the total energy $E$, its dependence with $\gamma$ is a purely quantum effect notably visible near the ground state energy, and for large energies differs for Markovian and non-Markovian regimes.

arXiv commentExtended version with additional clarifying information

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Cited by in corpus (7)

• Fluctuation-Dissipation Relation from the Nonequilibrium Dynamics of a Nonlinear Open Quantum System
• Quantum Thermodynamics and Quantum Coherence Engines
• Nonequilibrium Quantum Free Energy and Effective Temperature, Generating Functional and Influence Action
• Fluctuation-Dissipation Relation for Open Quantum Systems in Nonequilibrium Steady State
• Distinguishing pure and thermal states by Landauer's principle in open systems
• Some speculations about local thermalization of nonequilibrium extended quantum systems
• Zeroth Law in Quantum Thermodynamics at Strong Coupling: `in Equilibrium', not `Equal Temperature'