Straightforward quantum-mechanical derivation of the Crooks fluctuation theorem and the Jarzynski equality
arXiv:1202.4529 · doi:10.1103/PhysRevE.86.011111
Abstract
We obtain the Crooks and the Jarzynski non-equilibrium fluctuation relations using a direct quantum-mechanical approach for a finite system that is either isolated or coupled not too strongly to a heat bath. These results were hitherto derived mostly in the classical limit. The two main ingredients in the picture are the time-reversal symmetry and the application of the first law to the case where an agent performs work on the system. No further assumptions regarding stochastic or Markovian behavior are necessary, neither a master equation or a classical phase-space picture are required. The simplicity and the generality of these non-equilibrium relations are demonstrated, giving very simple insights into the Physics.
7 pages, 2 figures, pedagogical, improved version
References in corpus (8)
- Fluctuation theorems: Work is not an observable
- Dissipation: The phase-space perspective
- Quantum Trajectory Approach to the Stochastic Thermodynamics of a Forced Harmonic Oscillator
- Quantum Operation Time Reversal
- Fluctuation theorems in driven open quantum systems
- Quantum work relations and response theory
- Quantum and classical fluctuation theorems from a decoherent histories, open-system analysis
- Restricted quantum-classical correspondence and counting statistics for a coherent transition
Cited by in corpus (11)
- Jarzynski equality for quantum stochastic maps
- Non-equilibrium equalities with unital quantum channels
- Introducing one-shot work into fluctuation relations
- Quantum Work in the Bohmian framework
- Quantum driving and work
- Manipulating phonons of a trapped-ion system using optical tweezers
- Fluctuations of the heat exchanged between two quantum spin chains
- Semi-classical work and quantum work identities in Weyl representation
- Measuring work in quantum many-body systems using a dynamical "work agent"
- Heat exchange and fluctuation in Gaussian thermal states in the quantum realm
- Fluctuation theorems for autonomous work