Quantum thermodynamics from the nonequilibrium dynamics of open systems: energy, heat capacity and the third law

Abstract

We take the perspective of open quantum systems and examine from their nonequilibrium dynamics the conditions when the physical quantities, their relations and the laws of thermodynamics become well defined and viable for quantum many body systems. We first describe how an open system nonequilibrium dynamics (ONEq) approach is different from the closed combined system + environment in a global thermal state (CGTs) setup. Only after the open system equilibrates will it be amenable to conventional thermodynamics descriptions, thus quantum thermodynamics (QTD) comes at the end rather than assumed in the beginning. We see the open system approach having the advantage of dealing with nonequilibrium processes as many experiments in the near future will call for. Because it spells out the conditions of QTD's existence it can also aid us in addressing the basic issues in quantum thermodynamics from first principles in a systematic way. We then study one broad class of open quantum systems where the full nonequilibrium dynamics can be solved exactly, that of the quantum Brownian motion of $N$ strongly coupled harmonic oscillators, interacting strongly with a scalar field environment. Here we focus on the internal energy, heat capacity and the Third Law. We show for this class of physical models, amongst other findings, the extensive property of the internal energy, the positivity of the heat capacity and the validity of the Third Law from the perspective of the behavior of the heat capacity toward zero temperature. These conclusions obtained from exact solutions and quantitative analysis clearly disprove claims of negative specific heat in such systems and dispel allegations that in such systems the validity of the Third Law of thermodynamics relies on quantum entanglement.

67 pages, 6 figures; published version

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Cited by in corpus (39)

• {\it Colloquium:} Statistical Mechanics and Thermodynamics at Strong Coupling: Quantum and Classical
• Strong Coupling Thermodynamics of Open Quantum Systems
• Non-Markovianity and negative entropy production rates
• Steady-state entanglement and coherence of the coupled qubit system in equilibrium and nonequilibrium environments
• Nonequilibrium Thermodynamics of Quantum Friction
• Wading through the void: Exploring quantum friction and nonequilibrium fluctuations
• Thermodynamics of quantum systems strongly coupled to a heat bath I. Operator thermodynamic functions and relations
• A Nernst heat theorem for nonequilibrium jump processes
• Fluctuation-Dissipation Relation from the Nonequilibrium Dynamics of a Nonlinear Open Quantum System
• Quantum Thermodynamics and Quantum Coherence Engines
• Fluctuation-Dissipation and Correlation-Propagation Relations from the Nonequilibrium Dynamics of Detector-Quantum Field Systems
• Atom-Field Interaction: From Vacuum Fluctuations to Quantum Radiation and Quantum Dissipation / Radiation Reaction
• Nonequilibrium Quantum Free Energy and Effective Temperature, Generating Functional and Influence Action
• von Neumann entropy and the entropy production of a damped harmonic oscillator
• Nonequilibrium Nonlinear Open Quantum Systems I. Functional Perturbative Analysis of a Weakly Anharmonic Oscillator
• Fluctuation-Dissipation and Correlation-Propagation Relations in $(1+3)$D Moving Detector-Quantum Field Systems
• Fluctuation-Dissipation Relation for Open Quantum Systems in Nonequilibrium Steady State
• The vanishing of excess heat for nonequilibrium processes reaching zero ambient temperature
• Exact dynamics and thermalization of open quantum systems coupled to reservoir through particle exchanges
• Strong Coupling and non-Markovian Effects in the Statistical Notion of Temperature
• Quantum Parametric Oscillator Heat Engines in Squeezed Thermal Baths: Foundational Theoretical Issues
• Specific heat of a driven lattice gas
• Ground State Excitation of an Atom Strongly Coupled to a Free Quantum Field
• Quantum Thermodynamic Uncertainty Relations, Generalized Current Fluctuations and Nonequilibrium Fluctuation-Dissipation Inequalities
• Quantum work statistics at strong reservoir coupling
• Dynamical Response of an Unruh-DeWitt Detector in a Quantum Field over the History of the Universe
• Hot entanglement? -- Parametrically coupled quantum oscillators in two heat baths: instability, squeezing and driving
• Quantum corrections to the entropy in a driven quantum Brownian motion model
• Quantum dissipation of planar harmonic systems: Maxwell-Chern-Simons theory
• Quantum Radiation and Dissipation in Relation to Classical Radiation and Radiation Reaction
• Quantum Thermodynamic Uncertainties in Nonequilibrium Systems from Robertson-Schrödinger Relations
• Fluctuations-Induced Quantum Radiation and Reaction from an Atom in a Squeezed Quantum Field
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• Interference effects and modified Born rule in the presence of torsion