Classical and quantum thermodynamics described as a system-bath model: The dimensionless minimum work principle

Abstract

We formulate a thermodynamic theory applicable to both classical and quantum systems. These systems are depicted as thermodynamic system-bath models capable of handling isothermal, isentropic, thermostatic, and entropic processes. Our approach is based on the use of a dimensionless thermodynamic potential expressed as a function of the intensive and extensive thermodynamic variables. Using the principles of dimensionless minimum work and dimensionless maximum entropy derived from quasi-static changes of external perturbations and temperature, we obtain the Massieu-Planck potentials as entropic potentials and the Helmholtz-Gibbs potentials as free energy. These potentials can be interconverted through time-dependent Legendre transformations. Our results are verified numerically for an anharmonic Brownian system described in phase space using the low-temperature quantum Fokker-Planck equations in the quantum case and the Kramers equation in the classical case, both developed for the thermodynamic system-bath model. Thus, we clarify the conditions for thermodynamics to be valid even for small systems described by Hamiltonians and establish a basis for extending thermodynamics to non-equilibrium conditions.

19 pages, 4 figures, 7 tables

References in corpus (41)

• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Quantum Thermodynamic Cycles and quantum heat engines
• The Physics of Maxwell's demon and information
• Quantum heat engines and refrigerators: Continuous devices
• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• Quantum Equivalence and Quantum Signatures in Heat Engines
• Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model
• {\it Colloquium:} Statistical Mechanics and Thermodynamics at Strong Coupling: Quantum and Classical
• Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities
• Quantum Heat Engines Using Superconducting Quantum Circuits
• Quantum Thermodynamics: A Nonequilibrium Green's Functions Approach
• Entanglement Dynamics of Two Qubits in a Common Bath
• Virtual excitations in the ultra-strongly-coupled spin-boson model: physical results from unphysical modes
• Real-Time and Imaginary-Time Quantum Hierarchal Fokker-Planck Equations
• On the nature of heat in strongly coupled open quantum systems
• First and Second Law of Quantum Thermodynamics: A Consistent Derivation Based on a Microscopic Definition of Entropy
• Strong friction limit in quantum mechanics: the Quantum Smoluchowski equation
• A variational description of the quantum phase transition in the sub-Ohmic spin-boson model
• Quantum Heat Current under Non-perturbative and Non-Markovian Conditions: Applications to Heat Machines
• Analog of a quantum heat engine using a single-spin qubit
• Jarzynski Relations for Quantum Systems and Some Applications
• Non-Canonical Statistics of a Spin-Boson Model: Theory and Exact Monte-Carlo Simulations
• Violation of TUR in a periodically driven work-to-work converter from weak to strong dissipation
• Analysis of 2D THz-Raman spectroscopy using a non-Markovian Brownian oscillator model with nonlinear system-bath interactions
• Non-Markovian quantum thermodynamics: laws and fluctuation theorems
• Hierarchical Schrödinger Equations of Motion for Open Quantum Dynamics
• Quantum Suppression of Ratchet Rectification in a Brownian System Driven by a Biharmonic Force
• Low-Temperature Quantum Fokker-Planck and Smoluchowski Equations and Their Extension to Multistate Systems
• Cyclic quantum engines enhanced by strong bath coupling
• Unification of the first law of quantum thermodynamics
• Numerically "exact" simulations of a quantum Carnot cycle: Analysis using thermodynamic work diagrams
• Optical response of laser-driven charge-transfer complex described by Holstein-Hubbard model coupled to heat baths: Hierarchical equations of motion approach
• Numerically "exact" simulations of entropy production in the fully quantum regime: Boltzmann entropy versus von Neumann entropy
• Discretized hierarchical equations of motion in mixed Liouville--Wigner space for two-dimensional vibrational spectroscopies of liquid water
• Quantum field heat engine powered by phonon-photon interactions
• Dynamics of a strongly coupled quantum heat engine -- computing bath observables from the hierarchy of pure states
• Open Quantum Dynamics Theory for Non-Equilibrium Work: Hierarchical Equations of Motion Approach
• The laws of thermodynamics for quantum dissipative systems: A quasi-equilibrium Helmholtz energy approach
• Simulating two-dimensional correlation spectroscopies with third-order infrared and fifth-order infrared--Raman processes of liquid water
• Nonequilibrium work distributions in quantum impurity system-bath mixing processes

Cited by in corpus (5)

• Thermodynamic quantum Fokker-Planck equations and their application to thermostatic Stirling engine
• Hierarchical equations of motion for multiple baths (HEOM-MB) and their application to Carnot cycle
• Classical and quantum thermodynamics in a non-equilibrium regime: Application to Stirling engine
• Entropic witness for quantum memory in open system dynamics
• Testing bath correlation functions for open quantum dynamics simulations