Thermodynamics of quantum measurements

TL;DR

This paper explores the thermodynamics of quantum measurements, revealing how selective and non-selective measurements can power heat engines and the role of entropy and work in these processes.

Contribution

It introduces a unified framework for understanding the thermodynamics of quantum measurements, including the maximal work extractable and the implications for quantum heat engines.

Findings

Non-selective measurements can power heat engines despite increasing entropy.

The work difference between selective and non-selective measurements equals the reset work of the measurement device.

Reversible cycles can be achieved by replacing measurements with premeasurements and coupling to work sources.

Abstract

Quantum measurement of a system can change its mean energy, as well as entropy. A selective measurement (classical or quantum) can be used as a "Maxwell's demon" to power a single-temperature heat engine, by decreasing the entropy. Quantum mechanically, so can a non-selective measurement, despite increasing the entropy of a thermal state. The maximal amount of work extractable following the measurement is given by the change in free energy: $W_{max}^{(non-)sel.}=\Delta E_{meas}-T_{Bath}\Delta S_{meas}^{(non-)sel.}$. This follows from the "generalized 2nd law for nonequilibrium initial state" [Hasegawa et. al, PLA (2010)], of which an elementary reduction to the standard law is given here. It is shown that $W_{max}^{sel.}-W_{max}^{non-sel.}$ equals the work required to reset the memory of the measuring device, and that no such resetting is needed in the non-selective case. Consequently, a single-bath engine powered by either kind of measurement works at a net loss of $T_{Bath}\Delta S_{meas}^{non-sel}$ per cycle. By replacing the measurement by a reversible "premeasurement" and allowing a work source to couple to the system and memory, the cycle can be made completely reversible.