Characterizing Irreversibility in Open Quantum Systems

Abstract

Irreversibility is a fundamental concept with important implications at many levels. It pinpoints the fundamental difference between the intrinsically reversible microscopic equations of motion and the unidirectional arrow of time that emerges at the macroscopic level. More pragmatically, a full quantification of the degree of irreversibility of a given process can help in the characterisation of the performance of thermo-machines operating at the quantum level. Here, we review the concept of entropy production, which is commonly intended as the measure of thermodynamic irreversibility of a process, pinpointing the features and shortcomings of its current formulation.When watching a movie, a question that can be made is whether the movie was recorded in that way, or if we are watching a time-reversed version of the actual recording. In our everyday experience, this question is often easy to answer, because watching broken pieces of glass moving from the floor to the top of a table and assembling themselves in the shape of a cup just feels weird. It is much more likely that the movie-makers recorded a glass cup falling down and breaking. Even though we are able to reach this conclusion quickly, none of the fundamental laws of physics (e.g., Newtonian equations of motion) forbid the broken pieces to reassemble the cup. Only the second law of thermodynamics makes the argument that, as the broken pieces represent a system of larger entropy, the reassembling process is impossible or at least very unlikely.The above is only a simple example, taken from everyday life, of a much deeper concept, namely that the fundamental, microscopic equations of motion are symmetric under time-reversal, but the thermodynamical laws are not and establish a fundamental difference between past and future. This apparent paradox has been known under the name of the "arrow of time", given by Eddington in 1927 [1]. The understanding of the emergence of the arrow of time from underlying quantum dynamics, and the formalisation of a self-consistent framework for its characterisation have been the focus of much interest. On one hand, we are in great need of tools able to reveal, experimentally, the implications that nonequilibrium dynamics has on the degree of reversibility for a given quantum process. On the other hand, the tools that are currently available for the (even only theoretical) investigation of thermodynamic irreversibility lack the widespread applicability and logical selfcontained nature that is required from a complete theory. Let us elaborate more on this aspect.The entropy of an open system, unlike the energy, does not satisfy a continuity equation: in addition to entropic fluxes exchanged between a system and its environment, some entropy may also be produced within the system. This contribution is called entropy production and, according to the second law of thermodynamics, it is always non-negative, being zero only when the system and the environment are in thermal equilibrium. On the other hand, for closed systems that are d...

An out-of-equilibrium non-Markovian quantum heat engine

“…We now wish to investigate further the implications that the crossover from an adiabatic to a sudden-quench transformation has in the Markovian regime, focusing in particular on issues of thermodynamic irreversibility [58,59,60]. At the core of a study on irreversible thermodynamical transformation is the concept of irreversible entropy production and the closely related notion of irreversible work.…”

Thermodynamics from indistinguishability: Mitigating and amplifying the effects of the bath

“…Note that the therm ωns is due to our energy reference. The physically meaningful quantity is ∆F the variation of free energy, which give precious information on irreversibility of the transformation [79], but also on the quantity of extractable work [45]. Note that in our simple situation of a dissipation by a thermal bath the variation of free energy is equal to the bath temperature times the entropy production.…”

“…In order to avoid this unusual and "non-aesthetic" plot, we prefere to directly plot the graph of the entropy production Σ to obtain more insights on the irreversibility of the evolution. The entropy production, which is the core concept of the Second Law of thermodynamics, is simply given here by Σ = −β B ∆F [48,51,79]. Fig.…”

Quantum-Heat Fluctuation Relations in Three-Level Systems Under Projective Measurements

“…The evaluation of the relevant work originated by using a coherent modulation of the system Hamiltonian has been the subject of intense investigation [18][19][20][21][22][23][24]. A special focus was devoted to the study of heat and entropy production, obeying of the second law of thermodynamics, the interaction with one or more external bodies, and/or the inclusion of an observer [25][26][27][28][29][30][31][32][33][34].…”