Landauer’s Principle for Trajectories of Repeated Interaction Systems

Abstract

We analyze Landauer's principle for repeated interaction systems consisting of a reference quantum system S in contact with an environment E which is a chain of independent quantum probes. The system S interacts with each probe sequentially, for a given duration, and the Landauer principle relates the energy variation of E and the decrease of entropy of S by the entropy production of the dynamical process. We consider refinements of the Landauer bound at the level of the full statistics (FS) associated to a two-time measurement protocol of, essentially, the energy of E. The emphasis is put on the adiabatic regime where the environment, consisting of T 1 probes, displays variations of order T −1 between the successive probes, and the measurements take place initially and after T interactions. We prove a large deviation principle and a central limit theorem as T → ∞ for the classical random variable describing the entropy production of the process, with respect to the FS measure. In a special case, related to a detailed balance condition, we obtain an explicit limiting distribution of this random variable without rescaling. At the technical level, we obtain a non-unitary adiabatic theorem generalizing that of [HJPR17] and analyze the spectrum of complex deformations of families of irreducible completely positive trace-preserving maps.1 we will always set the Boltzmann constant to 1, so that β = 1/Θ, Θ the temperature.

Nonequilibrium dynamics with finite-time repeated interactions

“…For g x = g y = g and ω s = ω p , the system-probe interaction describes a resonant exchange of excitation that preserves the total energy. In other words, the resonant probes realize a channel of thermal operations that effectively models spin thermalization, as often noticed and exploited [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. This holds true for arbitrary system spin numbers J, see App.…”

“…The scattering operator (7) can then be Taylor-expanded to recover the known short-time master equation . However, the condition ω s τ 1 explicitly breaks the validity of the rotating wave approximation (RWA), as it makes a difference whether the full interaction Hamiltonian or only its resonant terms are plugged into the short-time operator (7).…”

“…Local equilibration, on the other hand, can be achieved with exchange interactions (g x = g y , G x = G y ) as in the single-spin case [10,11]. Specifically, the short-time scattering operator (7) is precisely that of a single spin interacting with a probe as before, and so the corresponding dissipator in the master equation (4) yields a local Gibbs state in that limit. At finite τ -values, indirect coupling contributions betweenĴ (2) and the probe start to appear in the scattering operator (2), implying that (4) does not resemble the local thermalization master equation.…”

A nonlinear quantum adiabatic approximation

“…Generalisations to non-self-adjoint generators were provided in J3,AFGG], leading to extensions to gapless, non self-adjoint generators provided in [Sc]. Also, formulations of the adiabatic approximation have been shown to hold true for unitary and non unitary discrete time evolutions, [DKS,Ta,HJPR1,HJPR2], and for extended many body systems [BDR]. From this perspective, we prove a generalisation of the adiabatic theorem to nonlinear non-autonomous evolution equations in a Hilbert space defined by (1.2) and (1.1).…”

Estatística de calor e trabalho em modelos colisionais

“…Instead of picturing all the interactions happening at the same time, CMs implement the bath as a sequence of little pieces (units or ancillae) which collide with the system and are then traced out to produce the system reduced dynamics. Such models have been largely explored recently [29,30,33,[53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70], with particular emphasis to the fact that they can recover local master equations (LMEs).…”