Thermodynamics of Quantum Measurement and the Demon's Arrow of Time

TL;DR

This paper explores the thermodynamics of a quantum measurement device controlled by a Maxwell's demon, analyzing discrete and continuous measurement processes and linking thermodynamic variables to the demon's perceived arrow of time.

Contribution

It introduces a detailed analysis of thermodynamic variables in quantum measurement devices, connecting them to information-theoretic measures of the demon's arrow of time, including exact finite-time statistics.

Findings

Thermodynamic variables are determined by the demon's perceived arrow of time.

Derived exact finite-time statistics of work, heat, and entropy in continuous measurements.

Linked thermodynamic quantities to information-theoretic measures of the demon's arrow of time.

Abstract

We discuss the thermodynamic aspects of a single qubit based device, powered by weak quantum measurements, and feedback controlled by a quantum Maxwell's demon. We discuss both discrete and time-continuous operation of the measurement based device at finite temperature of the reservoir. In the discrete example where a demon acquires information via discrete weak measurements, we find that the thermodynamic variables including the heat exchanged, extractable work, and the entropy produced are completely determined by an information theoretic measure of the demon's perceived arrow of time. We also discuss a realistic time-continuous operation of the device where the feedback is applied after a sequence of weak measurements. In the time-continuous limit, we derive the exact finite-time statistics of work, heat and entropy changes along individual quantum trajectories of the quantum measurement process, and relate them to the demon's arrow of time.