Quantum thermodynamics from the nonequilibrium dynamics of open systems: Energy, heat capacity, and the third law

Abstract

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.

Strong Coupling Thermodynamics of Open Quantum Systems

“…Out of the weak coupling regime, several attempts have been performed to formulate a thermodynamic framework, e.g. [34][35][36][37][38][39][40][41][42][43][44][45]. A possible approach [34,38,39] is suggested by fact that in the weak coupling regimė Q (w) (t) = −Tr[H R (t)ρ R (t)], as it can be easily proven from the von Neumann equation and the approximation H(t) ≃ H S (t) + H R in Eqs.…”

Atom-Field Interaction: From Vacuum Fluctuations to Quantum Radiation and Quantum Dissipation or Radiation Reaction

“…It might be useful at this point to make this statement: Although LRT has a more restricted specified condition than NEq, they both belong to open system set-ups, which is formally different from the close system set-up of eigenvalue thermalization. For a depiction of the differences between the two formulations, see, e.g., the Introduction of [45].…”

Fluctuation-dissipation and correlation-propagation relations in (1 + 3)D moving detector-quantum field systems

“…dimensional Minkowski space in [21,45] because in the coincident limit of spatial coordinates, the commutator of the field operator…”

“…The divergent contribution of the first term on the righthand will be absorbed into natural frequency renormalization and its finite part will contribute to the damping term, while the second term will account for the non-Markovian influence originated from the other detectors. A detailed treatment can be found in [21,25,45]. In short, the presence of damping term in linear dynamics inevitably implies that the late-time dynamics of the linear system is governed by the stochastic noise.…”

“…6 In principle, the issue of renormalization enters in the derivation of the power associated with the dissipation. See the discussion in [45]. A derivation can be found in the Appendix of [34].…”