Quantum Work in the Bohmian framework

TL;DR

This paper introduces a quantum trajectory-based method to define and analyze work fluctuations in quantum systems, extending classical concepts to the quantum regime and including effects of initial state mixtures and coherences.

Contribution

It presents a novel approach to quantum work distribution using phase space trajectories, applicable to general quantum evolutions with coherences.

Findings

Work distribution depends on initial state mixtures.

Method applies to any quantum evolution, including with coherences.

Demonstrated with a driven quantum harmonic oscillator.

Abstract

At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for example, is characterised by the ensemble of system trajectories in phase space and, by including the probabilities for various trajectories to occur, a work distribution can be constructed. However, without phase space trajectories, the task of constructing a work probability distribution in the quantum regime has proven elusive. Here we use quantum trajectories in phase space and define fluctuating work as power integrated along the trajectories, in complete analogy to classical statistical physics. The resulting work probability distribution is valid for any quantum evolution, including cases with coherences in the energy basis. We demonstrate the quantum work probability distribution and its properties with an exactly solvable example of a driven quantum harmonic oscillator. An important feature of the work distribution is its dependence on the initial statistical mixture of pure states, which is reflected in higher moments of the work. The proposed approach introduces a fundamentally different perspective on quantum thermodynamics, allowing full thermodynamic characterisation of the dynamics of quantum systems, including the measurement process.