Irreversible entropy production: From classical to quantum

Abstract

Entropy production is a key quantity in any finite-time thermodynamic process. It is intimately tied with the fundamental laws of thermodynamics, embodying a tool to extend thermodynamic considerations all the way to non-equilibrium processes. It is also often used in attempts to provide the quantitative characterization of logical and thermodynamic irreversibility, stemming from processes in physics, chemistry and biology. Notwithstanding its fundamental character, a unifying theory of entropy production valid for general processes, both classical and quantum, has not yet been formulated. Developments pivoting around the frameworks of stochastic thermodynamics, open quantum systems, and quantum information theory have led to substantial progress in such endeavour. This has culminated in the unlocking of a new generation of experiments able to address stochastic thermodynamic processes and the impact of entropy production on them. This paper aims to provide a compendium on the current framework for the description, assessment and manipulation of entropy production. We present both formal aspects of its formulation and the implications stemming from the potential quantum nature of a given process, including a detailed survey of recent experiments.

Closed-System Solution of the 1D Atom from Collision Model

“…Framing the CM into a closed-system approach can shed new light on the thermodynamical analysis. Indeed, the pure state of the full system provides access to the correlations between the qubit and the bath, and among different time units of the bath, possibly revealing the microscopic mechanism underlying the total entropy production [ 38 ].…”

“…dt ξ(t ) + t 0 dt ξ(t ) − γ ξ(t )e −iω q t a † (t )|0, g , (38) with ξ(t) = e −γt/2 t 0 dt e γt 2 +iω q t ξ(t ) . Let us notice that tracing Equation ( 38) over the field, we obtain the qubit's state derived in Refs.…”

Fluctuation theorem for irreversible entropy production in electrical conduction

“…The natural question arises, whether the two paradigms are consistent with each other, or rather whether the two "versions" of entropy production are equivalent. In particular, the occurrence of negative rates in irreversible thermodynamics [5,6,14] appears incompatible with the strict positivity of the stochastic entropy production rate often discussed in the literature [19][20][21][22][23][24][25][26][27][28][29][30][31][32].…”

Battery Charging in Collision Models with Bayesian Risk Strategies

“…This not only makes the dynamics simpler but also more controllable. For example, collisional models have proven to be crucial in developing the basic laws of thermodynamics in the quantum regime [ 5 , 6 , 7 , 8 ] or to further our understanding of non-Markovianity [ 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 ]. For a recent review, see [ 29 ].…”