# Quantum corrections of work statistics in closed quantum systems.

@article{Fei2018QuantumCO, title={Quantum corrections of work statistics in closed quantum systems.}, author={Zhaoyu Fei and Haitao Quan and Fei Liu}, journal={Physical review. E}, year={2018}, volume={98 1-1}, pages={ 012132 } }

We investigate quantum corrections to the classical work characteristic function (CF) as a semiclassical approximation to the full quantum work CF. In addition to explicitly establishing the quantum-classical correspondence of the Feynman-Kac formula, we find that these quantum corrections must be in even powers of ℏ. Exact formulas of the lowest corrections (ℏ^{2}) are proposed, and their physical origins are clarified. We calculate the work CFs for a forced harmonic oscillator and a forced… Expand

#### Figures and Topics from this paper

#### 7 Citations

Quantum corrections to the entropy and its application in the study of quantum Carnot engines.

- Physics, Medicine
- Physical review. E
- 2020

This work expands the von Neumann entropy in powers of ℏ by using the phase-space formulation, and the zeroth-order term reproduces the Gibbs entropy, and obtains the explicit expression of the quantum corrections of the entropy. Expand

Computing characteristic functions of quantum work in phase space.

- Physics, Medicine
- Physical review. E
- 2019

A numerical method that approximates the CFs to ℏ^{2} order is proposed and is exemplify the method with a time-dependent frequency harmonic oscillator and a family of quantum systems with time- dependent even power-law potentials. Expand

Path-integral approach to the calculation of the characteristic function of work.

- Physics, Medicine
- Physical review. E
- 2020

This study demonstrates the effectiveness of the path-integral approach for the calculation of work statistics in both quantum and classical thermodynamics, and brings important insights to the understanding of the trajectory work in quantum systems. Expand

Energy conservation and Jarzynski equality are incompatible for quantum work

- Physics
- 2021

Measuring the fluctuations of work in coherent quantum systems is notoriously problematic. Aiming to reveal the ultimate source of these problems, we demand of work measurement schemes the sheer… Expand

Symmetry and its breaking in a path-integral approach to quantum Brownian motion.

- Physics, Mathematics
- Physical review. E
- 2019

This work studies the Caldeira-Leggett model where a quantum Brownian particle interacts with an environment or a bath consisting of a collection of harmonic oscillators in the path-integral formalism and derives the influence functional explicitly in this setting, which captures the effect of the coupling to the bath. Expand

Nonequilibrium Green's Function's Approach to the Calculation of Work Statistics.

- Physics, Medicine
- Physical review letters
- 2020

This work proposes the contour-integral formulation for work statistics and shows how to do the perturbation expansion of the characteristic function of work and obtain the approximate expression of the CFW to the second order of the work parameter for an arbitrary system under a perturbative protocol. Expand

Semiclassical work and quantum work identities in Weyl representation

- Physics
- 2019

We derive a semi-classical nonequilibrium work identity by applying the Wigner-Weyl quantization scheme to the Jarzynski identity for a classical Hamiltonian. This allows us, to the leading order in… Expand

#### References

SHOWING 1-10 OF 66 REFERENCES

Quantum-to-classical transition in the work distribution for chaotic systems.

- Physics, Medicine
- Physical review. E
- 2017

A semiclassical approximation to the work distribution for a quench process in chaotic systems that provides a link between the quantum and classical work distributions and accurately describes the quantum distribution as the temperature is increased is developed. Expand

Derivation of quantum work equalities using a quantum Feynman-Kac formula.

- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2012

A method to derive nonequilibrium work equalities for isolated quantum systems, which include the Jarzynski equality and Bochkov-Kuzovlev equality is presented, which shows a higher similarity in form to the method deriving the fluctuation relations in the classical systems. Expand

Calculating work in adiabatic two-level quantum Markovian master equations: a characteristic function method.

- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2014

A characteristic function method is presented to calculate the probability density functions of the inclusive work in adiabatic two-level quantum Markovian master equations and finds that the fluctuation properties of the work can be described by the symmetry of the characteristic functions, which is exactly the same as in the case of isolated systems. Expand

Quantum-Classical Correspondence Principle for Work Distributions

- Physics
- 2015

For closed quantum systems driven away from equilibrium, work is often defined in terms of projective measurements of initial and final energies. This definition leads to statistical distributions of… Expand

Quantum-classical correspondence principle for work distributions in a chaotic system.

- Mathematics, Medicine
- Physical review. E
- 2016

Numerical results suggest that there exists a correspondence principle between quantum and classical work distributions in a chaotic system and justifies the definition of quantum work via two-point energy measurements. Expand

On the quantum correction for thermodynamic equilibrium

- Physics
- 1932

The probability of a configuration is given in classical theory by the Boltzmann formula exp [— V/hT] where V is the potential energy of this configuration. For high temperatures this of course also… Expand

Experimental reconstruction of work distribution and study of fluctuation relations in a closed quantum system.

- Physics, Medicine
- Physical review letters
- 2014

We report the experimental reconstruction of the nonequilibrium work probability distribution in a closed quantum system, and the study of the corresponding quantum fluctuation relations. The… Expand

Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems

- Physics
- 2009

Fluctuation theorems (FTs), which describe some universal properties of nonequilibrium fluctuations, are examined from a quantum perspective and derived by introducing a two-point measurement on the… Expand

Phase space representation of quantum dynamics

- Physics
- 2010

Abstract We discuss a phase space representation of quantum dynamics of systems with many degrees of freedom. This representation is based on a perturbative expansion in quantum fluctuations around… Expand

Statistics of work performed on a forced quantum oscillator.

- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2008

Various aspects of the statistics of work performed by an external classical force on a quantum mechanical system are elucidated for a driven harmonic oscillator and general fluctuation and work theorems holding for microcanonical and canonical initial states are confirmed. Expand