Nonequilibrium thermodynamics and many-body dynamics in open quantum systems

Jen-Tsung Hsiang, Chung-Hsien Chou, Yiğit Subaşı +1 more

In a series of papers, we intend to take the perspective of open quantum systems and examine from their nonequilibrium dynamics the conditions when the physical quantities, their relations, and the laws of thermodynamics become well defined and viable for quantum many-body systems. We first describe how an open-system nonequilibrium dynamics (ONEq) approach is different from the closed combined system + environment in a global thermal state (CGTs) setup. Only after the open system equilibrates will it be amenable to conventional thermodynamics descriptions, thus quantum thermodynamics (QTD) comes at the end rather than assumed in the beginning. The linkage between the two comes from the reduced density matrix of ONEq in that stage having the same form as that of the system in the CGTs. We see the open-system approach having the advantage of dealing with nonequilibrium processes as many experiments in the near future will call for. Because it spells out the conditions of QTD's existence, it can also aid us in addressing the basic issues in quantum thermodynamics from first principles in a systematic way. We then study one broad class of open quantum systems where the full nonequilibrium dynamics can be solved exactly, that of the quantum Brownian motion of N strongly coupled harmonic oscillators, interacting strongly with a scalar-field environment. In this paper, we focus on the internal energy, heat capacity, and the third law. We show for this class of physical models, amongst other findings, the extensive property of the internal energy, the positivity of the heat capacity, and the validity of the third law from the perspective of the behavior of the heat capacity toward zero temperature. These conclusions obtained from exact solutions and quantitative analysis clearly disprove claims of negative specific heat in such systems and dispel allegations that in such systems the validity of the third law of thermodynamics relies on quantum entanglement. They are conceptually and factually unrelated issues. Entropy and entanglement will be the main theme of our second paper on this subject matter.

Daniel Matos

Léa Ferreira dos Santos, Eduardo Jonathan Torres-Herrera

Vincenzo Alba, Federico Carollo

The spreading of information forms the basis of several quantum nonequilibrium phenomena, such as seen in the emergence of thermodynamics and statistical physics. Recently, much progress has been made in understanding the dynamics of information in isolated integrable systems after a quantum quench, by using a quasiparticle picture predicting ballistic spreading of quantum correlations. This paper shows how to apply these ideas to describe the dissipative dynamics of correlations and of entanglement in open quantum many-body systems.

Nicolas Bergmann, Michael Galperin

Abstract We give a nonequilibrium Green’s function (NEGF) perspective on thermodynamics formulations for open quantum systems that are strongly coupled to baths. A scattering approach implying thermodynamic consideration of a supersystem (system plus baths) that is weakly coupled to external superbaths is compared with the consideration of thermodynamics of a system that is strongly coupled to its baths. We analyze both approaches from the NEGF perspective and argue that the latter yields a possibility of thermodynamic formulation consistent with a dynamical (quantum transport) description.

Léa Ferreira dos Santos, Eduardo Jonathan Torres-Herrera