Calorimetric measurement of work for a driven harmonic oscillator

Sampaio, Rui; Suomela, Samu; Ala-Nissilä, Tapio

doi:10.1103/physreve.94.062122

Cited by 3 publications

(4 citation statements)

References 54 publications

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“…Substituting Eqs. (22,24) into Eq. ( 13) and integrating over the intermediate position x b , one can obtain the semiclassical propagator for the forward propagation…”

Section: Path-integral Approach To the Calculation Of Work Statistics...mentioning

confidence: 99%

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

et al. 2020

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Work statistics characterizes important features of a non-equilibrium thermodynamic process. But the calculation of the work statistics in an arbitrary non-equilibrium process is usually a cumbersome task. In this work, we study the work statistics in quantum systems by employing Feynman's path-integral approach. We derive the analytical work distributions of two prototype quantum systems. The results are proved to be equivalent to the results obtained based on Schrödinger's formalism. We also calculate the work distributions in their classical counterparts by employing the path-integral approach. Our study demonstrates the effectiveness of the path-integral approach to 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.

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“…Substituting Eqs. (22,24) into Eq. ( 13) and integrating over the intermediate position x b , one can obtain the semiclassical propagator for the forward propagation…”

Section: Path-integral Approach To the Calculation Of Work Statistics...mentioning

confidence: 99%

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

et al. 2020

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“…Recently, there has been growing interest in understanding the fluctuation of energy in open systems at the single-shot level of individual runs of an experimental protocol [4][5][6][7][8][9][10]. This scenario is commonly described by unraveling master equations, leading to a dynamical equation for the evolution of a stochastic wave function [1,11].…”

Section: Introductionmentioning

confidence: 99%

“…The natural generalization of the conditional energy is taken from Eq. (10) in the main text, namely…”

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confidence: 99%

Contributions to single-shot energy exchanges in open quantum systems

et al. 2019

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The exchange of energy between a classical open system and its environment can be analysed for a single run of an experiment using the phase space trajectory of the system. By contrast, in the quantum regime such energy exchange processes must be defined for an ensemble of runs of the same experiment based on the reduced system density matrix. Single-shot approaches have been proposed for quantum systems that are weakly coupled to a heat bath. However, a single-shot analysis for a quantum system that is entangled or strongly interacting with external degrees of freedom has not been attempted because no system wave function exists for such a system within the standard formulation of quantum theory. Using the notion of the conditional wave function of a quantum system, we derive here an exact formula for the rate of total energy change in an open quantum system, valid for arbitrary coupling between the system and the environment. In particular, this allows us to identify three distinct contributions to the total energy flow: an external contribution coming from the explicit time dependence of the Hamiltonian, an interaction contribution associated with the interaction part of the Hamiltonian, and an entanglement contribution, directly related to the presence of entanglement between the system and its environment. Given the close connection between weak values and the conditional wave function, the approach presented here provides a new avenue for experimental studies of energy fluctuations in open quantum systems.

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“…In this dynamical framework, a quantum analog of the Jarzynski relation can be proved by de ning a work operator through a generalization of the Feynman-Kac formula to quantum Markov semi-groups (see [32] and references therein). Further studies and proposals for experimental checks of the quantum Jarzynski identity have unveiled the interplay between measurement, quantum trajectories and stochastic thermodynamics [33][34][35][36][37][38][39][40][41][42][43][44][45][46].…”

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confidence: 99%

Semiclassical work and quantum work identities in Weyl representation

Brodier

Mallick

Almeida

2020

J. Phys. A: Math. Theor.

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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 , to overcome the problem of defining the concept of work in quantum mechanics. We propose a geometric interpretation of this semi-classical relation in terms of trajectories in a complex phase space and illustrate it with the exactly solvable case of the quantum harmonic oscillator. PACS numbers: 03.65.Sq,03.65.YzAccording to the second principle of thermodynamics, macroscopic phenomena tend to evolve towards states corresponding to a maximum number of underlying microstates, i.e. states that maximize entropy. Combined with the first principle, this leads to a more operational statement for isothermal processes: the minimal amount of work to modify a system from a state A to a state B is given bywhere F = U − T S is the free energy. Statistical mechanics has shown that the interpretation of macroscopic thermodynamics is statistical, by endowing microscopic states with a probability measure. Hence, the second principle should be understood as an average of a random process; one should write, in fact, ∂ 2 S ∂q f ∂q i 1/2 is of higher order in than the exponential of S.

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Calorimetric measurement of work for a driven harmonic oscillator

Cited by 3 publications

References 54 publications

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

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

Contributions to single-shot energy exchanges in open quantum systems

Semiclassical work and quantum work identities in Weyl representation

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