Natural nonequilibrium states in quantum statistical mechanics

Abstract

A quantum spin system is discussed, where a heat flow between infinite reservoirs takes place in a finite region. A time dependent force may also be acting. Our analysis is based on a simple technical assumption concerning the time evolution of infinite quantum spin systems. This assumption, physically natural but currently proved for few specific systems only, says that quantum information diffuses in space-time in such a way that the time integral of the commutator of local observables converges: ${\int }_{-\infty }^{0}dt||[B,{\alpha }^{t}A]||<\infty$. In this setup one can define a natural nonequilibrium state. In the time independent case, this nonequilibrium state retains some of the analyticity which characterizes KMS equilibrium states. A linear response formula is also obtained which remains true far from equilibrium. The formalism presented here does not cover situations where (for time independent forces) the time translation invariance and uniqueness of the natural nonequilibrium state are broken.

17 pages, 1 fig, numerous sign changes in this new version

References in corpus (3)

• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Non-Equilibrium Statistical Mechanics of Anharmonic Chains Coupled to Two Heat Baths at Different Temperatures
• Entropy Production in Non-Linear, Thermally Driven Hamiltonian Systems

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• Exponential Convergence to Non-Equilibrium Stationary States in Classical Statistical Mechanics
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• Theory of Non-Equilibrium Sationary States as a Theory of Resonances
• Nonequilibrium, thermostats and thermodynamic limit
• How should one define entropy production for nonequilibrium quantum spin systems?
• Adiabatic non-equilibrium steady states in the partition free approach
• Repeated and continuous interactions in open quantum systems
• Nonequilibrium transport through quantum-wire junctions and boundary defects for free massless bosonic fields
• Relative entropy and entropy production for equilibrium states in pAQFT
• Broken translation invariance in quasifree fermionic correlations out of equilibrium
• Stationary states in infinite volume with non zero current
• Quantum states from mixtures of equilibrium distributions