We address, on the example of a simple solvable model, the issue of whether the stationary state of dissipative systems converges to an equilibrium state in the low dissipation limit. We study a driven dissipative Zero Range Process on a tree, in which particles are interpreted as finite amounts of energy exchanged between degrees of freedom. The tree structure mimicks the hierarchy of length scales; energy is injected at the top of the tree ('large scales'), transferred through the tree and dissipated mostly in the deepest branches of the tree ('small scales'). Varying a parameter characterizing the transfer dynamics, a transition is observed, in the low dissipation limit, between a quasi-equilibrated regime and a far-from-equilibrium one, where the dissipated flux does not vanish.
We consider the stationary measure of the dissipative dynamical system in a finite volume. A finite dissipation, however small, generally makes the measure singular, while at zero dissipation the measure is constant. Thus dissipative part of the dynamics is a singular perturbation producing an infinite change in the measure. This is a result of the infinite time of evolution that enhances the small effects of dissipation to form singularities. We show how to deal with the singularity of the perturbation and describe the statistics of the measure. We derive all the correlation functions and the…
We construct a global Lindblad master equation for a Kitaev quantum wire of finite length, weakly coupled to an arbitrary number of thermal baths, within the Born-Markov and secular approximations. We find that the coupling of an external bath to more than one lattice site generates quantum interference effects, arising from the possibility of fermions to tunnel through multiple paths. In the presence of two baths at different temperatures and/or chemical potentials, the steady-state particle current can be expressed through the Landauer-Büttiker formula, as in a ballistic transport setup, wit…
It is shown, that Bose-Einstein condensation can occur not only in spatially extended equilibrium systems, but also in the systems far from thermal equilibrium, which show order-disorder phase transition. The investigation is performed by solving the Complex Ginzburg-Landau equation, a universal model for nonequilibrium order-disorder phase transitions.
We introduce a solvable stochastic model inspired by granular gases for driven dissipative systems. We characterize far from equilibrium steady states of such systems through the non-Boltzmann energy distribution and compare different measures of effective temperatures. As an example we demonstrate that fluctuation-dissipation relations hold, however with an effective temperature differing from the effective temperature defined from the average energy.
Driven quantum systems coupled to an environment typically exhibit effectively thermal behavior with relaxational dynamics near criticality. However, a different qualitative behavior might be expected in the weakly dissipative limit due to the competition between coherent dynamics and weak dissipation. In this work, we investigate a driven-dissipative infinite-range Ising model in the presence of individual atomic dissipation, a model that emerges from the paradigmatic open Dicke model in the large-detuning limit. We show that the system undergoes a dynamical crossover from relaxational dynami…
We study the fate of the Ising model and its universal properties when driven by a rapid periodic drive and weakly coupled to a bath at equilibrium. The far from equilibrium steady-state regime of the system is accessed by means of a Floquet mean field approach. We show that, depending on the details of the bath, the drive can strongly renormalize the critical temperature to higher temperatures, modify the critical exponents, or even change the nature of the phase transition from second to first order after the emergence of a tricritical point. Moreover, by judiciously selecting the frequency …
Maximum Caliber (Max Cal) is purported to be a general variational principle for Non-Equilibrium Statistical Physics (NESP). But recently, Jack and Evans and Maes have raised concerns about how Max Cal handles dissipative processes. Here, we show that the problem does not lie in Max Cal; the problem is in the use of insufficient constraints. We also present an exactly solvable single-particle model of dissipation, valid far from equilibrium, and its solution by Maximum Caliber. The model illustrates how the influx and efflux of work and heat into a flowing system alters the distribution of tra…
A system far from equilibrium is characterized by unconventional many-body dynamical effects, which can lead to anomalous density fluctuations and mass transport. Interestingly, these structural and dynamic features often emerge simultaneously in driven dissipative systems. Here we seek an origin of their co-existence by numerical simulations of a two-dimensional driven granular gas. We reveal a causal link between superdiffusive transport and giant density fluctuations. The kinetic dissipation upon particle collisions depends on the relative velocity of colliding particles, and is responsible…
We present a new approach to far-from-equilibrium statistical mechanics, based on the concept of generalized entropy, which is a microscopically-defined generalization of Onsager-Machlup functional. In the case when a set of slow (adiabatic) variables can be chosen, our formalism yields a general form of the macroscopic evolution law (Generalized Langevin Equation) and extends Fluctuation Dissipative Theorem. It also provides for a simple understanding of recently-discovered Fluctuation Theorem
This work presents new parallelizable numerical schemes for the integration of Dissipative Particle Dynamics with Energy conservation (DPDE). So far, no numerical scheme introduced in the literature is able to correctly preserve the energy over long times and give rise to small errors on average properties for moderately small timesteps, while being straightforwardly parallelizable. We present in this article two new methods, both straightforwardly parallelizable, allowing to correctly preserve the total energy of the system. We illustrate the accuracy and performance of these new schemes both…
Driven-dissipative systems define a broad class of non-equilibrium systems where an external drive (e.g. laser) competes with a dissipative environment. The steady state of dynamics is generically distinct from a thermal state characteristic of equilibrium. As a representative example, a driven-dissipative system with a continuous symmetry is generically disordered in two dimensions in contrast with the well-known algebraic order in equilibrium XY phases. In this paper, we study a 2D driven-dissipative model of weakly interacting bosons with a continuous $U(1)$ symmetry. Our aim is two-fold: F…
In this paper we report that notions of topological protection can be applied to stationary configurations that are driven far from equilibrium by active, dissipative processes. We show this for physically two disparate cases : stochastic networks governed by microscopic single particle dynamics as well as collections of driven, interacting particles described by coarse-grained hydrodynamic theory. In both cases, the presence of dissipative couplings to the environment that break time reversal symmetry are crucial to ensuring topologically protection. These examples constitute proof of princip…
The fluctuation-dissipation (F-D) theorem is a fundamental result for systems near thermodynamic equilibrium, and justifies studies between microscopic and macroscopic properties. It states that the nonequilibrium relaxation dynamics is related to the spontaneous fluctuation at equilibrium. Most processes in Nature are out of equilibrium, for which we have limited theory. Common wisdom believes the F-D theorem is violated in general for systems far from equilibrium. Recently we show that dynamics of a dissipative system described by stochastic differential equations can be mapped to that of a …
The thermodynamic uncertainty relations (TURs), originally discovered for classical systems, dictate the trade-off between dissipation and fluctuations of irreversible current, specifying a minimal bound that constrains the two quantities. In a series of effort to extend the relation to the one under more generalized conditions, it has been noticed that the bound is less tight in open quantum processes. To study the origin of the loose bounds, we consider an external field-driven transition dynamics of two-level quantum system weakly coupled to the bosonic bath as a model of open quantum syste…
Ever since the insight spreaded that tailored dissipation can be employed to control quantum systems and drive them towards pure states, the field of non-equilibrium quantum mechanics gained remarkable momentum. So far research focussed on emergent phenomena caused by the interplay and competition of unitary Hamiltonian and dissipative Markovian dynamics. In this manuscript we zero in on a so far rather understudied aspect of open quantum systems and non-equilibrium physics, namely the utilization of purely dissipative couplings to explore pure quantum phases and non-equilibrium phase transiti…
Bose-Einstein condensation, the macroscopic occupation of a single quantum state, appears in equilibrium quantum statistical mechanics and persists also in the hydrodynamic regime close to equilibrium. Here we show that even when a degenerate Bose gas is driven into a steady state far from equilibrium, where the notion of a single-particle ground state becomes meaningless, Bose-Einstein condensation survives in a generalized form: the unambiguous selection of an odd number of states acquiring large occupations. Within mean-field theory we derive a criterion for when a single and when multiple …
