Jarzynski equation for a simple quantum system: Comparing two definitions of work

Abstract

The validity of the Jarzynski equation for a very simple, exactly solvable quantum system is analyzed. The implications of two different definitions of work proposed in the literature are investigated. The first one derives from measurements of the system energy at the beginning and at the end of the process under consideration making the work a classical stochastic variable with transition probabilities derived from quantum mechanics. In the second definition an operator of work is introduced and the average in the Jarzynski equation is a quantum expectation value. For the first definition a general quantum mechanical version of the Jarzynski equation is known to hold. For the second one the Jarzynski equation fails to yield the free energy difference at low temperature.

5 papes, 1 figure largly rewritten and slightly enlarged version

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Cited by in corpus (40)

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• {\it Colloquium:} Statistical Mechanics and Thermodynamics at Strong Coupling: Quantum and Classical
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• Fully quantum fluctuation theorems
• Full distribution of work done on a quantum system for arbitrary initial states
• Quantum Fluctuation Relations for the Lindblad Master Equation
• The quantum-classical correspondence principle for work distributions
• Assessing the non-equilibrium thermodynamics in a quenched quantum many-body system via single projective measurements
• Probing Quantum Interference Effects in the Work Distribution
• Work and its fluctuations in a driven quantum system
• Introducing one-shot work into fluctuation relations
• Work as an external quantum observable and an operational quantum work fluctuation theorem
• Moments of work in the two-point measurement protocol for a driven open quantum system
• Quantum Work in the Bohmian framework
• Jarzynski Equality for Driven Quantum Field Theories
• Quantum fluctuation theorems and power measurements
• An autonomous quantum machine to measure the thermodynamic arrow of time
• Quantum driving and work
• A unified approach to the derivation of work theorems for equilibrium and steady-state, classical and quantum Hamiltonian systems
• Quantum optomechanical straight-twin engine
• Optimal protocols for Hamiltonian and Schrödinger dynamics
• Model Studies on the Quantum Jarzynski Relation
• Fluctuations of work in nearly adiabatically driven open quantum systems
• Quasi-probabilities of work and heat in an open quantum system
• Fluctuating work in coherent quantum systems: proposals and limitations
• Functional field integral approach to quantum work
• Quantum mean-square predictors and thermodynamics
• Measuring energy by measuring any other observable
• Fluctuation theorems for genuine quantum mechanical regimes
• Nonequilibrium work equalities in isolated quantum systems
• Path integral approach to the calculation of the characteristic function of work
• Ancilla-assisted measurement of quantum work
• The distribution of work performed on a NIS junction
• Quasistatic work processes: When slowness implies certainty
• Operational work fluctuation theorem for open quantum systems
• Calorimetric measurement of quantum work
• Calculation of semiclassical free energy differences along non-equilibrium classical trajectories
• Quantum work statistics in regular and classical-chaotic dynamical billiard systems
• Counting statistics of energy transport across squeezed thermal reservoirs