Entropy production and asymptotic factorization via thermalization: A collisional model approach

Abstract

The Markovian evolution of an open quantum system is characterized by a positive entropy production, while the global entropy gets redistributed between the system and the environment degrees of freedom. Starting from these premises, we analyze the entropy variation of an open quantum system in terms of two distinct relations: the Clausius inequality, that provides an intrinsic bound for the entropy variation in terms of the heat absorbed by the system, and an extrinsic inequality, which instead relates the former to the corresponding entropy increment of the environment. By modeling the thermalization process with a Markovian collisional model, we compare and discuss the two bounds, showing that the latter is asymptotically saturated in the limit of large interaction time. In this regime not only the reduced density matrix of the system reaches an equilibrium configuration, but it also factorizes from the environment degrees of freedom. This last result is proven analytically when the system-bath coupling is sufficiently strong and through numerical analysis in the weak-coupling regime.

Autonomous thermal machine for amplification and control of energetic coherence

“…It is also worth pointing out that, due to the repeated interaction scheme, the correlations continuously generated between the machine and the TLA may result in the generation of correlations between output atoms. This effect has been indeed recently reported for a simpler thermalization collisional model [50]. Also, very recent results concerning the possibility of distillation of coherence in a quantum thermodynamical framework [51] suggest that the local amplification reported here must be accompanied by the generation of such correlations.…”

Thermodynamics of Minimal Coupling Quantum Heat Engines

“…Furthermore, one can specify the character of the contact with the heat bath -it may be given by interaction Hamiltonian, or in terms of master equation of GKLS type [25][26][27][28]. Recently, a collisional model of an engine with heat baths was also used where the bath is composed of independent systems which one by one interact with the working body [29] (see also [30] for the comprehensive introduction into the topic and [31][32][33] for recent developments). As a matter of fact, this kind of modeling of the contact with bath fits into a recently widespread paradigm of thermal operations [34][35][36][37].…”

Entropy Production in Open Systems: The Predominant Role of Intraenvironment Correlations

“…Whenever this assumption holds, the result relating the entropy production to the displacement of the environment from equilibrium D[ρ E (t)||ρ eq E ] rather than the system-environment mutual information I SE is general and solid (since the Araki-Lieb inequality is universally valid). Therefore, although our numerical analysis focuses on the system with a time-independent Hamiltonian, this result holds also for externally driven systems, as well as setups described within the repeated interaction framework [4,[32][33][34][35][36] (in which the environment is made of independently prepared units interacting sequentially with the system). When, on the other hand, the entropy production is saturated at value smaller or comparable to 2 ln N (which may be true, e.g., for systems undergoing thermalization [36] or short interaction quench [21]) the relative importance of the terms D[ρ E (t)||ρ eq E ] and I SE may be not given by any general rule; instead, it may depend on details of the systemenvironment dynamics.…”