Quantum engine efficiency bound beyond the second law of thermodynamics

Abstract

According to the second law, the efficiency of cyclic heat engines is limited by the Carnot bound that is attained by engines that operate between two thermal baths under the reversibility condition whereby the total entropy does not increase. Quantum engines operating between a thermal and a squeezed-thermal bath have been shown to surpass this bound. Yet, their maximum efficiency cannot be determined by the reversibility condition, which may yield an unachievable efficiency bound above unity. Here we identify the fraction of the exchanged energy between a quantum system and a bath that necessarily causes an entropy change and derive an inequality for this change. This inequality reveals an efficiency bound for quantum engines energised by a non-thermal bath. This bound does not imply reversibility, unless the two baths are thermal. It cannot be solely deduced from the laws of thermodynamics.

Global Passivity in Microscopic Thermodynamics

“…Here, the state is fixed or given by the initial preparation of the setup, and we are interested in operators that are passive with respect to it. In that sense, the present approach is complementary to the one usually used in the literature on passivity [16][17][18][19][20]27].…”

“…Passivity [16][17][18][19][20]27] is defined as follows: a timeindependent operator A and a density matrix ρ are said to be passive with respect to each other if (i) ρ and A are diagonal in the same basis (same eigenvectors) and (ii) in a basis sorted in increasing order of eigenvalues of A, the eigenvalues of ρ are decreasing. Since the eigenvalues of ρ correspond to probabilities, it implies that when measuring A in a system prepared in a passive state, higher eigenvalues of A are less probable to be observed than lower eigenvalues.…”

“…Motivated by work extraction, in previous studies of passivity [16][17][18][19][20]27] the operator A was the Hamiltonian of the system (or of the environment [20]). The use of passivity in this paper is different from the standard one in three different ways.…”

“…In the current setup the most relevant form of the second law is the Clausius inequality (CI). In the following, we show that the concept of passivity [16][17][18][19][20] can be extended and can be used to derive additional inequalities. These inequalities have several appealing features not exhibited by the CI: (1) they hold for systems that have some initial quantum or classical correlation to the environment, (2) they can set upper and lower bounds on the system-environment correlation buildup, and (3) they allow us to derive families of inequalities that can detect external tempering in the form of heat leaks or feedback (e.g., a Maxwell demon) even when the CI fails to detect the external intervention.…”

Squeezed Environment Boosts Engine Performance

“…In the future, the exploitation of novel sources of work could have a large impact on the design of efficient and powerful engines at the microscale and nanoscale. By employing nonequilibrium reservoirs, it is expected that the efficiency of work generation can surpass standard thermodynamic bounds, as has been theoretically suggested for quantum coherent [12], quantum correlated [13,14], quantum-measurement-induced [15][16][17], and squeezed thermal reservoirs [18][19][20][21][22][23]. The realization of such engines not only extends our knowledge of finite-size, nonequilibrium, and quantum effects in thermodynamics, but could also lead to important applications in nanotechnology and in the life sciences [24].…”