Abstract We derive the basic laws of phenomenological non-equilibrium thermodynamics for small open systems, whose quantum nature can no longer be neglected. Emphasis is put from the beginning on deriving them from an underlying microscopic system on deriving them from an underlying microscopic system–bath picture. Commonly considered approximation schemes (wea k coupling master equations) are reviewed and their thermodynamics is studied. The zeroth law is discussed for small systems and exact identities for the entropy production, valid at strong coupling and in the non non-Markovian regime, are introduced. We discu ss the effect of finite baths even out of equilibrium and use the framework of repeated interactions to study microscopic non-equilibrium resources. The chapter concludes with the study of particle transport and thermoelectric devices, which were realized in experiments. This chapter focuses entirely on the dynamics of a system coupled to a bath without any external interventions.
The counterintuitive Mpemba effect, wherein a hotter system cools faster, critically lacks a general macroscopic theory. Here, starting from linear irreversible thermodynamics, we formulate a generalized Newton's cooling law,
dT/dt=−[γ0+MQ(t)](T−Tr), for a system at temperature
T relaxing in a thermal reservoir at
Tr, where the bare relaxation rate
γ0 is modified by an initial-state memory term,
Q(t)∝T(0)−Tr. Arising from the interplay between heat flux and structural evolution, the coefficient
M governs anomalous relaxation behaviors, where
M>0 (
M<0) induces the (inverse) Mpemba effect. This universal thermodynamic framework maps out phase diagram to provide general criteria for the Mpemba effect in complex systems, offering a macroscopic picture that bridges disparate microscopic approaches.
The circumstances under which a system reaches thermal equilibrium, and how to derive this from basic dynamical laws, has been a major question from the very beginning of thermodynamics and statistical mechanics. Despite considerable progress, it remains an open problem. Motivated by this issue, we address the more general question of equilibration. We prove, with virtually full generality, that reaching equilibrium is a universal property of quantum systems: almost any subsystem in interaction with a large enough bath will reach an equilibrium state and remain close to it for almost all times. We also prove several general results about other aspects of thermalization besides equilibration, for example, that the equilibrium state does not depend on the detailed microstate of the bath.
Ground-state cooling and pure state preparation of a small object that is embedded in a thermal environment is an important challenge and a highly desirable quantum technology. This paper proves, with two different methods, that a fundamental constraint on the cooling dynamic implies that it is impossible to cool, via a unitary system-bath quantum evolution, a system that is embedded in a thermal environment down to its ground state, if the initial state is a factorized product of system and bath states. The latter is a crucial but artificial assumption included in numerous tools that treat system-bath dynamics, such as master equation approaches and Kraus operator based methods. Adopting these approaches to address ground state and even approximate ground state cooling dynamics should therefore be done with caution, considering the fundamental theorem exposed in this work.
We investigate a system of two interacting qubits having one of them isolated and the other coupled to a thermal reservoir. We consider two different models of system-reservoir interaction: i) a model, in which the master equation is derived taking into account the interaction between the two subsystems (qubits), ii) a naive model, in which the master equation consists of a dissipative term added to the unitary evolution term. We study the dynamics of quantities such as bipartite entanglement, quantum discord and the linear entropy of the isolated qubit for both strong and weak coupling regimes (qubit-qubit interaction) as well as for different temperatures of the reservoir. We find significant disagreements between the results obtained from the two models even in the weak coupling regime. For instance, we show that according to the phenomenological model, the isolated qubit would approach a maximally mixed state more slowly for higher temperatures (unphysical result), while the microscopic model predicts the opposite behaviour (correct result).