Quantum fluctuation theorems and power measurements

TL;DR

This paper explores an alternative quantum work definition based on power measurements, analyzing its differences from the conventional energy measurement approach and its implications for fluctuation theorems.

Contribution

It introduces a power-based work measurement in quantum systems, compares it with the traditional energy measurement approach, and examines its statistical properties and relation to fluctuation theorems.

Findings

Power-based work differs from TEMA work in quantum systems.

The Jarzynski relation generally does not hold for power-based work.

Quantum Zeno effect causes trivial statistics with frequent power measurements.

Abstract

Work in the paradigm of the quantum fluctuation theorems of Crooks and Jarzynski is determined by projective measurements of energy at the beginning and end of the force protocol. In analogy to classical systems, we consider an alternative definition of work given by the integral of the supplied power determined by integrating up the results of repeated measurements of the instantaneous power during the force protocol. We observe that such a definition of work, in spite of taking account of the process dependence, has different possible values and statistics from the work determined by the conventional two energy measurement approach (TEMA). In the limit of many projective measurements of power, the system's dynamics is frozen in the power measurement basis due to the quantum Zeno effect leading to statistics only trivially dependent on the force protocol. In general the Jarzynski relation is not satisfied except for the case when the instantaneous power operator commutes with the total Hamiltonian at all times. We also consider properties of the joint statistics of power-based definition of work and TEMA work in protocols where both values are determined. This allows us to quantify their correlations. Relaxing the projective measurement condition, weak continuous measurements of power are considered within the stochastic master equation formalism. Even in this scenario the power-based work statistics is in general not able to reproduce qualitative features of the TEMA work statistics.