Nonequilibrium quantum bounds to Landauer's principle: Tightness and effectiveness

TL;DR

This paper compares two non-equilibrium quantum Landauer bounds, analyzing their tightness and effectiveness in a simple model, revealing the dominant role of populations and the limited impact of coherences.

Contribution

It provides a detailed comparison of entropic and thermodynamic quantum Landauer bounds, highlighting their limitations and extending findings to generic interactions.

Findings

Population terms dominate bound tightness

Coherences mainly affect the entropic bound

Both bounds can be weaker than Clausius' law

Abstract

We assess two different non-equilibrium quantum Landauer bounds: the traditional approach based on the change in entropy, referred to as the `entropic bound', and one based on the details of the dynamical map, referred to as the `thermodynamic bound'. By first restricting to a simple exactly solvable model of a single two level system coupled to a finite dimensional thermal environment and by exploiting an excitation preserving interaction, we establish the dominant role played by the population terms in dictating the tightness of these bounds with respect to the dissipated heat, and clearly establish that coherences only affect the entropic bound. Furthermore, we show that sharp boundaries between the relative performance of the two quantities emerge, and find that there are clear instances where both approaches return a bound weaker than Clausius' statement of the second law, rendering them ineffective. Finally we show that our results extend to generic interaction terms.