Path integral approach to quantum thermodynamics
arXiv:1708.05113 · doi:10.1103/PhysRevLett.121.040602
Abstract
Work belongs to the most basic notions in thermodynamics but it is not well understood in quantum systems, especially in open quantum systems. By introducing a novel concept of work functional along individual Feynman path, we invent a new approach to study thermodynamics in the quantum regime. Using the work functional, we derive a path-integral expression for the work statistics. By performing the expansion, we analytically prove the quantum-classical correspondence of the work statistics. In addition, we obtain the quantum correction to the classical fluctuating work. We can also apply this approach to an open quantum system in the strong coupling regime described by the quantum Brownian motion model. This approach provides an effective way to calculate the work in open quantum systems by utilizing various path integral techniques. As an example, we calculate the work statistics for a dragged harmonic oscillator in both isolated and open quantum systems.
arXiv comment7 pages, 3 figures (supplemental material: 6 pages). (v2) removed the discussion about heat, which appears in arXiv:1805.02815 . Changed the title
References in corpus (41)
- 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
- Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
- Continuous Quantum Phase Transitions
- Colloquium. Quantum Fluctuation Relations: Foundations and Applications
- Path ensembles averages in systems driven far-from-equilibrium
- 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
- Fluctuation Theorem for Arbitrary Open Quantum Systems
- Extracting quantum work statistics and fluctuation theorems by single qubit interferometry
- Quantum and Information Thermodynamics: A Unifying Framework based on Repeated Interactions
- Fundamental Aspects of Quantum Brownian Motion
- Observing a quantum Maxwell demon at work
- First and Second Law of Thermodynamics at strong coupling
- Path-integral analysis of fluctuation theorems for general Langevin processes
- 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
- Otto refrigerator based on a superconducting qubit: classical and quantum performance
- Information-to-work conversion by Maxwell's demon in a superconducting circuit-QED system
- A Quantum Fluctuation Theorem
- Wave Function Evolution of a Dissipative System
- 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
- 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
- Statistics of work performed on a forced quantum oscillator
- Quantum-Classical Correspondence Principle for Work Distributions in a Chaotic System
- Inertial Effects in Nonequilibrium Work Fluctuations by a Path Integral Approach
- Work measurement in an optomechanical quantum heat engine
- Quantum and classical fluctuation theorems from a decoherent histories, open-system analysis
- Quantum jump model for a system with a finite-size environment
- Calculating work in adiabatic two-level quantum Markovian master equations: A characteristic function method
- Path integral analysis of Jarzynski's equality: Analytical results
- 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 (48)
- Quantum Engines and Refrigerators
- Quantum heat statistics with time-evolving matrix product operators
- Fluctuation Theorems for a Quantum Channel
- Heat and work along individual trajectories of a quantum bit
- Quantum Coherence in a Quantum Heat Engine
- Path-integral methodology and simulations of quantum thermal transport: Full counting statistics approach
- Work as an external quantum observable and an operational quantum work fluctuation theorem
- Quantum Martingale Theory and Entropy Production
- Path integral approach to heat in quantum thermodynamics
- Group-theoretical approach to the calculation of quantum work distribution
- Quantum Fluctuation Theorems
- Inelastic thermoelectric transport and fluctuations in mesoscopic system
- Thermodynamics of decoherence
- Out-of-time-ordered correlation functions in open systems: A Feynman-Vernon influence functional approach
- Work distribution in thermal processes
- Nonequilibrium Green's function's approach to the calculation of work statistics
- Photonic heat transport across a Josephson junction
- Quantifying the validity and breakdown of the overdamped approximation in stochastic thermodynamics: Theory and experiment
- Entropy and information flow in quantum systems strongly coupled to baths
- Quantum-classical correspondence principle for heat distribution in quantum Brownian motion
- Heat distribution in open quantum systems with maximum entropy production
- Functional field integral approach to quantum work
- Theoretical formulations on thermodynamics of quantum impurity systems
- Work statistics in non-Hermitian evolutions with Hermitian endpoints
- Computing characteristic functions of quantum work in phase space
- Energy conservation and fluctuation theorem are incompatible for quantum work
- Efficiency of optically pumping a quantum battery and a two-stroke heat engine
- Hierarchical structure of fluctuation theorems for a driven system in contact with multiple heat reservoirs
- The Fluctuation-Dissipation Relations: Growth, Diffusion, and Beyond
- Entropy production of a small quantum system under strong coupling with an environment: A computational experiment
- Three heats in strongly coupled system and bath
- Semi-classical work and quantum work identities in Weyl representation
- Symmetry and its breaking in path integral approach to quantum Brownian motion
- Quantum work statistics at strong reservoir coupling
- Path integral approach to the calculation of the characteristic function of work
- Temperature fluctuations in mesoscopic systems
- Nonadiabatic evolution and thermodynamics of a time-dependent open quantum system
- Quantum corrections to the entropy in a driven quantum Brownian motion model
- A convenient Keldysh contour for thermodynamically consistent perturbative and semiclassical expansions
- Heat statistics in the relaxation process of the Edwards-Wilkinson elastic manifold
- Quantum stochastic thermodynamics in the mesoscopic-leads formulation
- On a tilted Liouville-master equation of open quantum systems
- Unifying quantum stochastic methods using Wick's theorem on the Keldysh contour
- Quantum heat transport and effects of quantum thermal devices in noncommuting coupled spins
- Structure of Quantum Mean Force Gibbs States for Coupled Harmonic Systems
- Exact density matrix elements for a driven dissipative system described by a quadratic Hamiltonian
- Quantum dynamics evolution predicted by the long short-term memory network in the photosystem II reaction center
- Dissipative adaptation in a driven spin-boson model within the path-integral formalism