Thermodynamics of quantum systems strongly coupled to a heat bath I. Operator thermodynamic functions and relations

Abstract

The thermodynamics of small quantum many-body systems strongly coupled to a heat bath at low temperatures with non-Markovian behavior are new challenges for quantum thermodynamics, as traditional thermodynamics is built on large systems vanishingly weakly coupled to a non-dynamical reservoir. Important also are the quantum attributes, as in quantum coherence, correlations, entanglement and fluctuations. All told, one needs to reexamine the meaning of the thermodynamic functions, the viability of the thermodynamic relations and the validity of the thermodynamic laws anew. In one popular approach to quantum thermodynamics the closed system, comprising the system of interest and the bath it is strongly coupled to, is assumed to be in a global thermal state throughout. In this set-up three theories of thermodynamics at strong coupling have been proposed, those of Gelin & Thoss [1], Seifert [2] and Jarzynski [3]. This paper provides a quantum formulation of them, with Jarzynski's two different representations encompassing the former two. Operator thermodynamic potentials and thermodynamic relations are presented. We mention issues related to energy and entropy in the two representations, a possible way to define quantum work in our functional formulation, and how to connect with the open system nonequilibrium dynamics approach to quantum thermodynamics, as proposed in [4].

44 pages

References in corpus (11)

• Foundation of Statistical Mechanics under experimentally realistic conditions
• Fluctuation Theorem for Arbitrary Open Quantum Systems
• Quantum Thermodynamics: A Nonequilibrium Green's Functions Approach
• Finite quantum dissipation: the challenge of obtaining specific heat
• Specific heat anomalies of open quantum systems
• Stochastic thermodynamics in the strong coupling regime: An unambiguous approach based on coarse-graining
• Thermodynamics of a subensemble of a canonical ensemble
• Information and entropy in quantum Brownian motion: Thermodynamic entropy versus von Neumann entropy
• Entanglement Energetics at Zero Temperature
• Quantum thermodynamics from the nonequilibrium dynamics of open systems: energy, heat capacity and the third law
• Heat due to system-reservoir correlations in thermal equilibrium

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• Non-Markovianity and negative entropy production rates
• Quantum thermodynamics from the nonequilibrium dynamics of open systems: energy, heat capacity and the third law
• Measurability of nonequilibrium thermodynamics in terms of the Hamiltonian of mean force
• Thermodynamics of Quantum Causal Models: An Inclusive, Hamiltonian Approach
• Green's functions perspective on nonequilibrium thermodynamics of open quantum systems strongly coupled to baths
• Nonequilibrium Quantum Free Energy and Effective Temperature, Generating Functional and Influence Action
• Entropy and information flow in quantum systems strongly coupled to baths
• Quantum Thermodynamics in the Refined Weak Coupling Limit
• Nonequilibrium Nonlinear Open Quantum Systems I. Functional Perturbative Analysis of a Weakly Anharmonic Oscillator
• Dynamics of a strongly coupled quantum heat engine -- computing bath observables from the hierarchy of pure states
• Strong Coupling Quantum Thermodynamics far away from Equilibrium: Non-Markovian Transient Quantum Heat and Work
• Fluctuation-Dissipation and Correlation-Propagation Relations in $(1+3)$D Moving Detector-Quantum Field Systems
• Relating Heat and Entanglement in Strong Coupling Thermodynamics
• Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems
• On the role of initial coherence in the spin phase-space entropy production rate
• Quantum Thermodynamic Uncertainties in Nonequilibrium Systems from Robertson-Schrödinger Relations
• A room temperature optomechanical squeezer
• Thermalization of isolated quantum many-body system and the role of entanglement
• Zeroth Law in Quantum Thermodynamics at Strong Coupling: `in Equilibrium', not `Equal Temperature'
• Intrinsic Entropy of Squeezed Quantum Fields and Nonequilibrium Quantum Dynamics of Cosmological Perturbations
• Work and heat exchanged during sudden quenches of strongly coupled quantum systems
• Structure of Quantum Mean Force Gibbs States for Coupled Harmonic Systems