Path integral approach to heat in quantum thermodynamics
arXiv:1805.02815 · doi:10.1103/PhysRevE.98.012113
Abstract
We study the heat statistics of a quantum Brownian motion described by the Caldeira-Leggett model. By using the path integral approach, we introduce a novel concept of the quantum heat functional along every pair of Feynman paths. This approach has an advantage of improving our understanding about heat in quantum systems. First, we demonstrate the microscopic reversibility of the system by connecting the heat functional to the forward and its time-reversed probabilities. Second, we analytically prove the quantum-classical correspondence of the heat functional and their statistics, which allows us to obtain better intuitions about the difference between classical and quantum heat.
arXiv comment11 pages, 1 figure
References in corpus (28)
- A nonequilibrium equality for free energy differences
- Stochastic thermodynamics, fluctuation theorems, and molecular machines
- The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
- Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
- Colloquium. Quantum Fluctuation Relations: Foundations and Applications
- Quantum Thermodynamics
- Fundamental limitations for quantum and nano thermodynamics
- Fluctuation theorems: Work is not an observable
- Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System
- Quantum and Information Thermodynamics: A Unifying Framework based on Repeated Interactions
- Fundamental Aspects of Quantum Brownian Motion
- First and Second Law of Thermodynamics at strong coupling
- Fluctuation theorem in quantum heat conduction
- Quantum jump approach for work and dissipation in a two-level system
- Quantum Trajectory Approach to the Stochastic Thermodynamics of a Forced Harmonic Oscillator
- A Quantum Fluctuation Theorem
- Fluctuation theorems in driven open quantum systems
- Quantum Heat Current under Non-perturbative and Non-Markovian Conditions: Applications to Heat Machines
- Energy exchange in driven open quantum systems at strong coupling
- The quantum-classical correspondence principle for work distributions
- General Non-Markovian structure of Gaussian Master and Stochastic Schrödinger Equations
- Path integral approach to quantum thermodynamics
- Open system trajectories specify fluctuating work but not heat
- Functional Integral approach to time-dependent heat exchange in open quantum systems: general method and applications
- Quantum-Classical Correspondence Principle for Work Distributions in a Chaotic System
- Quantum and classical fluctuation theorems from a decoherent histories, open-system analysis
- On work and heat in time-dependent strong coupling
- Transmission spectrum of a tunneling particle interacting with dynamical fields: real-time functional-integral approach
Cited by in corpus (20)
- Open quantum system dynamics and the mean force Gibbs state
- Quantum Brownian Motion for Magnets
- Path-integral methodology and simulations of quantum thermal transport: Full counting statistics approach
- Numerically "exact" simulations of a quantum Carnot cycle: Analysis using thermodynamic work diagrams
- An operator derivation of the Feynman-Vernon theory, with applications to the generating function of bath energy changes and to anharmonic baths
- Nonequilibrium Green's function's approach to the calculation of work statistics
- von Neumann entropy and the entropy production of a damped harmonic oscillator
- Quantum-classical correspondence principle for heat distribution in quantum Brownian motion
- Generalized Quantum Fluctuation Theorem for Energy Exchange
- Computing characteristic functions of quantum work in phase space
- Thermal power of heat flow through a qubit
- Hierarchical structure of fluctuation theorems for a driven system in contact with multiple heat reservoirs
- Symmetry and its breaking in path integral approach to quantum Brownian motion
- Temperature fluctuations in mesoscopic systems
- Temperature-heat uncertainty relation in nonequilibrium quantum thermometry
- Quantum corrections to the entropy in a driven quantum Brownian motion model
- A convenient Keldysh contour for thermodynamically consistent perturbative and semiclassical expansions
- Quantum stochastic thermodynamics in the mesoscopic-leads formulation
- Heat statistics in the relaxation process of the Edwards-Wilkinson elastic manifold
- Dissipative adaptation in a driven spin-boson model within the path-integral formalism