Full counting statistics approach to the quantum non-equilibrium Landauer bound

Abstract

We develop the full counting statistics of dissipated heat to explore the relation with Landauer's principle. Combining the two-time measurement protocol for the reconstruction of the statistics of heat with the minimal set of assumptions for Landauer's principle to hold, we derive a general one-parameter family of upper and lower bounds on the mean dissipated heat from a system to its environment. Furthermore, we establish a connection with the degree of non-unitality of the system's dynamics and show that, if a large deviation function exists as stationary limit of the above cumulant generating function, then our family of lower and upper bounds can be used to witness and understand first-order dynamical phase transitions. For the purpose of demonstration, we apply these bounds to an externally pumped three level system coupled to a finite sized thermal environment.

Quantum work statistics and resource theories: Bridging the gap through Rényi divergences

“…A similar set of one-parameter bounds was recently derived in the context of Landauer erasure [40]. For negative values η < 0, a family of upper bounds β W τ ≤ βΦ(η, τ )/|η| is obtained instead.…”

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

“…Our analysis is based on the FCS formalism developed in Ref. [26] with the time-convolutionless (TCL) type of quantum master equation [29,30]. With this formalism, we show that the above summarized trends of the bounds reported in Ref.…”

“…Apart from the conventional studies based on information theory, recent studies show that other approaches relying on nonequilibrium dynamics may also provide a thermodynamic lower bound [25,26]. This bound was first derived by studying a dynamical map represented by the Lindblad operator and employing a nonequilibrium fluctuation relation for the heat [25].…”

“…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.…”

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

“…Thus recently, several studies have explored lower bounds on the dissipated heat in a variety of systems, including the experimental tests of Landauer's principle [5][6][7][8], examining the validity of Landauer's bound for a fully quantum setting [4], its behavior in open quantum systems [9,10], schemes to minimize the dissipated heat [11], and a rigorous tightening of Landauer's bound [12]. While Landauer's principle is rooted in the use of information-theoretic entropies [1,2,12], recent studies have shown that other approaches that do not necessarily invoke any information theoretic tools but rather rely on the dynamics of the system, can be used to derive a "nonequilibrium thermodynamic" lower bound on the dissipated heat [13,14]. The relevance of this approach further relies on the fact that a microscopic analysis of the erasing procedure allows to take into account effects related to non-Markovianity or initial correlations [15], which have often shown to lead to counterintuitive phenomena [16,17].…”