Open quantum system dynamics and the mean force Gibbs state

Abstract

The dynamical convergence of a system to the thermal distribution, or Gibbs state, is a standard assumption across all of the physical sciences. The Gibbs state is determined just by temperature and the system's energies alone. But at decreasing system sizes, i.e. for nanoscale and quantum systems, the interaction with their environments is not negligible. The question then arises: Is the system's steady state still the Gibbs state? And if not, how may the steady state depend on the interaction details? Here we provide an overview of recent progress on answering these questions. We expand on the state-of-the-art along two general avenues: First we take the static point-of-view which postulates the so-called mean force Gibbs state. This view is commonly adopted in the field of strong coupling thermodynamics, where modified laws of thermodynamics and non-equilibrium fluctuation relations are established on the basis of this modified state. Second, we take the dynamical point-of-view, originating from the field of open quantum systems, which examines the time-asymptotic steady state within two paradigms. We describe the mathematical paradigm which proves return to equilibrium, i.e. convergence to the mean force Gibbs state, and then discuss a number of microscopic physical methods, particularly master equations. We conclude with a summary of established links between statics and equilibration dynamics, and provide an extensive list of open problems. This comprehensive overview will be of interest to researchers in the wider fields of quantum thermodynamics, open quantum systems, mesoscopic physics, statistical physics and quantum optics, and will find applications whenever energy is exchanged on the nanoscale, from quantum chemistry and biology, to magnetism and nanoscale heat management.

Tensor network simulation of chains of non-Markovian open quantum systems

“…We use a coupling strength α = 0.32 and cutoff frequency ω c = 4.0. Perturbation theory predicts that in a weak coupling limit, α → 0, the reduced chain density matrix of the full thermal state differs from the Gibbs state of the chain Hamiltonian at a quadratic order in the bath coupling [24]. We confirm this and present the results in the SM [48].…”

“…Single bath weak coupling limit.-Perturbation theory predicts that in a weak coupling limit the reduced chain density matrix of the full thermal state differs from the Gibbs state of the chain Hamiltonian at a quadratic order in the bath coupling [24]. The dimensionless coupling strength α is proportional to the square of the bath coupling amplitudes |g k | the chain thermalizes with the bath in the long time limit, we thus expect to find a difference between the reduced steady state and the Gibbs state of the chain Hamiltonian that is proportional to α in a weak coupling limit.…”

“…A popular approach to the study of thermalization of a subsystem is based on obtaining its reduced density matrix [20][21][22][23][24]. The reduced density matrix is, however, only a small fraction of the operationally accessible information of an open system.…”

Quantum Thermal Transport Beyond Second Order with the Reaction Coordinate Mapping

“…The coupling between the RCs and the residual baths are given by Ohmic spectral density functions post mapping, see Eq. (7). Furthermore, all parameters carry the same meaning as in the generalized spin-boson Hamiltonian, Eq.…”

“…Perturbative quantum master equation (QME) techniques are commonly used for studying quantum dissipative systems due to their simplicity and potential for analytical insights 3,7 . In particular, the popular Redfield approach relies on the Born approximation (as well as other assumptions), where the system-environment coupling strength λ is assumed weak.…”