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

Abstract

We assess two different nonequilibrium 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.

Lower bounds for the mean dissipated heat in an open quantum system

“…With this formalism, we show that the above summarized trends of the bounds reported in Ref. [28] also hold even for an open quantum system with an infinite recurrence time.…”

“…We now provide an analytic justification of these features using the structure of the matrix (20) and the identities Eqs. (26)- (28). From the expression of B en (t ) in Eq.…”

“…Despite their different origins, both bounds are valid and hence stimulated successive comparative studies on their tightness [25,26,28]. These studies have been performed for exactly solvable systems within a finite environment.…”

“…In particular, in Ref. [28], the authors systematically studied the dependence of the bounds on the initial state of a single spin-1/2 system contacting with another single spin-1/2 "environment" thereby clarifying the following difference: The thermodynamic bound depends only on the initial population, whereas the entropic bound is relevant to the initial coherence. As a result, they found the appearance of a sharp boundary at which the relative tightness switches.…”

Role of quantum coherence in the thermodynamics of energy transfer

“…[37]. The performance of quantum coherence has been analyzed in the context of work extraction [38][39][40][41][42], entropy production [43,44], and Landauer's erasure [45]. Other investigations focus on how coherence transforms under thermodynamic operations [46][47][48], without intending to assign it some operational meaning.…”