Thermodynamic arrow of time of quantum projective measurements

TL;DR

This paper explores the thermodynamic arrow of time in quantum systems under projective measurements, using Jensen-Shannon divergence to quantify time asymmetry and its dependence on temperature and system dynamics.

Contribution

It introduces a novel framework linking quantum measurements to thermodynamic time asymmetry via information-theoretic measures, revealing temperature-dependent behaviors.

Findings

High-temperature energy fluctuations lead to zero time asymmetry.

Low-temperature ground state survival limits time asymmetry below ln 2.

Repeated measurements reach a fixed point of time asymmetry.

Abstract

We investigate a thermodynamic arrow associated with quantum projective measurements in terms of the Jensen-Shannon divergence between the probability distribution of energy change caused by the measurements and its time reversal counterpart. Two physical quantities appear to govern the asymptotic values of the time asymmetry. For an initial equilibrium ensemble prepared at a high temperature, the energy fluctuations determine the convergence of the time asymmetry approaching zero. At low temperatures, finite survival probability of the ground state limits the time asymmetry to be less than $\ln 2$. We illustrate our results for a concrete system and discuss the fixed point of the time asymmetry in the limit of infinitely repeated projections.