We report the statistical properties of the fluctuations of the energy flux in an electronic RC circuit driven with a stochastic voltage. The fluctuations of the power injected in the circuit are measured as a function of the damping rate and the forcing parameters. We show that its distribution exhibits a cusp close to zero and two asymmetric exponential tails, the asymmetry being driven by the mean dissipation. This simple experiment allows to capture the qualitative features of the energy flux distribution observed in more complex dissipative systems. We also show that the large fluctuations of injected power averaged on a time lag do not verify the Fluctuation Theorem even for long averaging time. This is in contrast with the findings of previous experiments due to their small range of explored fluctuation amplitude. The injected power in a system of N components either correlated or not is also studied to mimic systems with large number of particles, such as in a dilute granular gas.
The probability operator for a generic non-equilibrium quantum system is derived. The corresponding stochastic, dissipative Schrödinger equation is also given. The dissipative and stochastic propagators are linked by the fluctuation-dissipation theorem that is derived from the unitary condition on the time propagator. The dissipative propagator is derived from thermodynamic force and entropy fluctuation operators that are in general non-linear.
Dissipative particle dynamics (DPD) is a relatively new technique which has proved successful in the simulation of complex fluids. We caution that for the equilibrium achieved by the DPD simulation of a simple fluid the temperature depends strongly on the time step. An analytic expression for the dependence is obtained and shown to agree well with simulation results.
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 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 characteriz…
The stochastic differential equations for a model of dissipative particle dynamics, with both total energy and total momentum conservation at every time-step, are presented. The algorithm satisfies detailed balance as well as the fluctuation-dissipation theorems that ensure that the proper thermodynamic equilibrium can be reached. Macroscopic equilibrium probability distributions as well as equations of state for the model are also derived, and an appropriate definition of the free energy of the system is consistently proposed. Several simulations results of equilibrium as well as transport pr…
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 connection between dissipation and symmetry breaking is a long-standing enigma in statistical physics. It is intimately connected to the quest of a non-equilibrium functional whose minimization gives the non-equilibrium steady state (NESS). Writing down such a functional, we show that, in the presence of additive noise, any NESS is characterized by the minimum entropy production compatible with the maximum dissipation along cycles in the trajectory space. This result sheds light on the excess entropy production principle and the onset of chiral symmetry breaking out-of-equilibrium, indicat…
Conservation laws constrain the stationary state statistics of driven dissipative systems because the average flux of a conserved quantity between driving and dissipation scales should be constant. This requirement leads to a universal scaling law for flux-measuring correlation functions, which generalizes the 4/5-th law of Navier-Stokes turbulence. We demonstrate the utility of this simple idea by deriving new exact scaling relations for models of aggregating particle systems in the fluctuation-dominated regime and for energy and wave action cascades in models of strong wave turbulence.
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…
Using the path integral approach to equilibrium statistical physics the effect of dissipation on Landau diamagnetism is calculated. The calculation clarifies the essential role of the boundary of the container in which the electrons move. Further, the derived result for diamagnetization also matches with the expression obtained from a time-dependent quantum Langevin equation in the asymptotic limit, provided a certain order is maintained in taking limits. This identification then unifies equilibrium and nonequilibrium statistical physics for a phenomenon like diamagnetism, which is inherently …
An explicit demonstration is given of a harmonic oscillator in equilibrium approaching the equilibrium of a corresponding interacting system by coupling it to a thermal bath consisting of a continuum of harmonic oscillators.
We prove the existence and uniqueness of an equilibrium state with unit mass to the dissipative linear Boltzmann equation with hard--spheres collision kernel describing inelastic interactions of a gas particles with a fixed background. The equilibrium state is a universal Maxwellian distribution function with the same velocity as field particles and with a non--zero temperature lower than the background one, which depends on the details of the binary collision. Thanks to the H--theorem we then prove strong convergence of the solution to the Boltzmann equation towards the equilibrium.
We apply a new method based upon thermofield dynamics (TFD) to study entanglement of finite-spin systems with non-competitive external fields for both equilibrium and non-equilibrium cases. For the equilibrium finite-spin systems, the temperature dependence of the extended density matrices is derived using this method, and the effect of non-competitive external field is demonstrated. For the non-equilibrium finite-spin systems, the time dependence of the extended density matrices and the extended entanglement entropies is derived in accordance with von Noumann equation, and the dissipative dyn…
We study the out-of-equilibrium dynamics of dissipative gases of atoms excited to two or more high-lying Rydberg states. This situation bears interesting similarities to classical binary (in general $p$-ary) mixtures of particles. The effective forces between the components are determined by the inter-level and intra-level interactions of Rydberg atoms. These systems permit to explore new parameter regimes which are physically inaccessible in a classical setting, for example one in which the mixtures exhibit non-additive interactions. In this situation the out-of-equilibrium evolution is chara…
We study the dissipative dynamics of a charged oscillator in a magnetic field by coupling (a la Caldeira and Leggett) it to a heat bath consisting of non-interacting harmonic oscillators. We derive here the auto-correlation functions of the position and momentum and study its behavior at various limiting situations. The equilibrium (steady state) dispersions of position and momentum are obtained from their respective autocorrelation functions. We analyse the equilibrium position and momentum dispersions at low and high temperatures for both low and high magnetic field strengths. We obtain the …
We investigate the non-equilibrium dynamics of a driven-dissipative spin ensemble with competing power-law interactions. We demonstrate that dynamical phase transitions as well as bistabilities can emerge for asymptotic van der Waals interactions, but critically rely on the presence of a slower decaying potential-core. Upon introducing random particle motion, we show that a finite gas temperature can drive a phase transition with regards to the spin degree of freedom and eventually leads to mean-field behaviour in the high-temperature limit. Our work reconciles contrasting observations of rece…
In this work we compare and characterize the behavior of Langevin and Dissipative Particle Dynamics (DPD) thermostats in a broad range of non-equilibrium simulations of polymeric systems. Polymer brushes in relative sliding motion, polymeric liquids in Poiseuille and Couette flows, and brush-melt interfaces are used as model systems to analyze the efficiency and limitations of different Langevin and DPD thermostat implementations. Widely used coarse-grained bead-spring models under good and poor solvent conditions are employed to assess the effects of the thermostats. We considered equilibrium…
Chaos is usually referred to the sensitivity to initial conditions in which the nonlinearity plays a crucial role. Beyond such a mathematical description, the understanding of the underlying physical origin of the chaos is still not very clear. Here we study the dissipative chaos from the perspective of the nonequilibrium dynamics. This was not fully investigated in the traditional chaos theory, despite of the Lorenz's original discovery of chaos from the nonequilibrium atmosphere. We found that the nonequilibriumness as the degree of detailed balance breaking can be quantified by the appearan…
We have investigated the time-evolution of a free particle in interaction with a phonon thermal bath, using the tight-binding approach. A dissipative quantum walk can be defined and many important non-equilibrium decoherence properties can be investigated analytically. The non-equilibrium statistics of a pure initial state have been studied. Our theoretical results indicate that the evolving wave-packet shows the suppression of Anderson's boundaries (ballistic peaks) by the presence of dissipation. Many important relaxation properties can be studied quantitatively, such as von Neumann's entrop…
We construct a microscopic theory of applying a heat flow from thermostatted boundary walls in the film geometry. We treat a classical one-component fluid, but our method is applicable to any fluids and solids. We express linear response of any variable ${\cal B}$ in terms of the time-correlation functions between $\cal B$ and the heat flows ${\cal J}_K$ from the thermostats to the particles. Furthermore, the surface variables ${\cal J}_K$ can be written in the form of space integrals of bulk quantities from the equations of motion. Owing to this surface-to-bulk relation, the steady-state resp…
The macroscopic hydrodynamic equations are derived for many-body systems in the local-equilibrium approach, using the Schrödinger picture of quantum mechanics. In this approach, statistical operators are defined in terms of microscopic densities associated with the fundamentally conserved quantities and other slow modes possibly emerging from continuous symmetry breaking, as well as macrofields conjugated to these densities. Functional identities can be deduced, allowing us to identify the reversible and dissipative parts of the mean current densities, to obtain general equations for the time …
A novel experimental paradigm and a novel modelling approach are presented to investigate oscillatory human motor performance by means of a key concept from condensed matter physics, namely, thermodynamic state variables. To this end, in the novel experimental paradigm participants performed pendulum swinging movements at self-selected oscillation frequencies in contrast to earlier studies in which pacing signals were used. Moreover, in the novel modelling approach, a canonical-dissipative limit cycle oscillator model was used with a conservative part that accounts for nonharmonic oscillator c…
The theory of continuous phase transitions predicts the universal collective properties of a physical system near a critical point, which for instance manifest in characteristic power-law behaviours of physical observables. The well-established concept at or near equilibrium, universality, can also characterize the physics of systems out of equilibrium. The most fundamental instance of a genuine non-equilibrium phase transition is the directed percolation universality class, where a system switches from an absorbing inactive to a fluctuating active phase. Despite being known for several decade…
Precessing ball solitons (PBS) in a ferromagnet during the first order phase transition induced by a magnetic field directed along the axis of anisotropy, while the action of the periodic field perpendicular to the main magnetic field, have been analyzed. Under this condition, the characteristics of arising equilibrium PBS's are uniquely determined by the frequency of the periodic field, but the solitons with other frequencies are impossible. It is shown that the equilibrium PBS's are essentially the "dissipative structures" that can arise in a metastable state.
We investigate the out-of-equilibrium behavior of a dissipative gas of Rydberg atoms that features a dynamical transition between two stationary states characterized by different excitation densities. We determine the structure and properties of the phase diagram and identify the universality class of the transition, both for the statics and the dynamics. We show that the proper dynamical order parameter is in fact not the excitation density and find evidence that the dynamical transition is in the "model A" universality class, i.e. it features a non-trivial $\mathbb{Z}_2$ symmetry and a dynam…
We study the non-equilibrium dynamics of driven spin lattices in the presence of decoherence caused by either laser phase noise or strong decay. In the first case, we discriminate between correlated and uncorrelated noise and explore their effect on the mean density of Rydberg states and the full counting statistics (FCS). We find that while the mean density is almost identical in both cases, the FCS differ considerably. The main method employed is the Langevin equation (LE) but for the sake of efficiency in certain regimes, we use a Markovian master equation and Monte Carlo rate equations, re…
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…
In macroscopic systems behavior is usually reproducible and fluctuations, which are deviations from the typically observed mean values, are small. But almost all inverse problems in the physical and biological sciences are ill-posed and these fluctuations are highly 'amplified'. Using stochastic thermodynamics we describe a system in equilibrium kicked to a state far from equilibrium and the following dissipative process back to equilibrium. From the observed value at a certain time after the kick the magnitude of the kick should be estimated, which is such an ill-posed inverse problem and flu…
A two-dimensional system of particles with tunable repulsive interactions is experimentally investigated. Soft ferromagnetic particles are placed on a vibrating rough plate and vertically confined, so that they perform a horizontal Brownian motion in a cell. When immersed in an external vertical magnetic field, the particles become magnetised and thus interact according to a dipolar repulsive law. As the amplitude of the magnetic field is increased, magnetic repulsion raises and the rate of inelastic collisions decreases. Studying the pair correlation function and the particle velocity distrib…
Smoothed Dissipative Particle Dynamics (SDPD) is a mesoscopic method which allows to select the level of resolution at which a fluid is simulated. In this work, we study the consistency of the resulting thermodynamic properties as a function of the size of the mesoparticles, both at equilibrium and out of equilibrium. We also propose a reformulation of the SDPD equations in terms of energy variables. This increases the similarities with Dissipative Particle Dynamics with Energy conservation and opens the way for a coupling between the two methods. Finally, we present a numerical scheme for SDP…
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 …
Studying the role of activity parameters and the nature of time-symmetric path-variables constitutes an important part of nonequilibrium physics, so we argue. The relevant variables are residence times and the undirected traffic between different states. Parameters are the reactivities, escape rates and accessibilities and how those possibly depend on the imposed driving. All those count in the frenetic contribution to statistical forces, response and fluctuations, operational even in the stationary distribution when far enough from equilibrium. As these time-symmetric aspects can vary indepen…
Coherence is a defining feature of quantum condensates. These condensates are inherently multimode phenomena and in the macroscopic limit it becomes extremely difficult to resolve populations of individual modes and the coherence between them. In this work we demonstrate non-equilibrium Bose-Einstein condensation (BEC) of photons in a sculpted dye-filled microcavity, where threshold is found for $8\pm 2$ photons. With this nanocondensate we are able to measure occupancies and coherences of individual energy levels of the bosonic field. Coherence of individual modes generally increases with inc…
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…
The nonexponential relaxation and aging inherent to complex dynamics manifested in a wide variety of dissipative systems is analyzed through a model of diffusion in phase space in the presence of a nonconservative force. The action of this force establishes a heat flow which maintains the system away from equilibrium. The inability of the system to find its equilibrium state becomes apparent through the presence of an effective temperature field. This is the temperature of the stationary nonequilibrium state reached by the system satisfying a generalyzed version of the fluctuation-dissipation …
Fluctuation-dissipation relations (FDRs) and time-reversal symmetry (TRS), two pillars of statistical mechanics, are both broken in generic driven-dissipative systems. These systems rather lead to non-equilibrium steady states far from thermal equilibrium. Driven-dissipative Ising-type models, however, are widely believed to exhibit effective thermal critical behavior near their phase transitions. Contrary to this picture, we show that both the FDR and TRS are broken even macroscopically at, or near, criticality. This is shown by inspecting different observables, both even and odd operators un…
A simple and transparent derivation of the formally exact probability distribution for classical non-equilibrium systems is given. The corresponding stochastic, dissipative equations of motion are also derived.
We study by means of numerical simulations the model of dissipative particle dynamics with energy conservation for the simple case of thermal conduction. It is shown that the model displays correct equilibrium fluctuations and reproduces Fourier law. The connection between "mesoscopic coarse graining" and "resolution" is clarified.
We study the equilibrium dynamics of a single polymer chain under good solvent condition. Special emphasis is laid on varying the drag force experienced by the chain while it moves. To this end we model the solvent in a mesoscopic manner by employing the Lowe-Andersen approach of dissipative particle dynamics which is known to reproduce hydrodynamic effects. Our approach captures the correct static behavior in equilibrium. Regarding the dynamics, we investigate the scaling of the self-diffusion coefficient $D$ with respect to the length of the polymer $N$, yielding results that are compatible …
We address the effects of dissipative defects giving rise to a localized particle loss, in one-dimensional non-interacting lattice fermionic gases confined within a region of size $\ell$. We consider homogeneous systems within hard walls and inhomogeneous systems where the particles are trapped by space-dependent external potentials, such as harmonic traps. We model the dissipative particle-decay mechanism by Lindblad master equations governing the time evolution of the density matrix. The resulting quantum dynamics is analyzed in protocols starting from the ground state of the Hamiltonian for…
We present a numerical method to simulate non-equilibrium Floquet steady states of one-dimensional periodically-driven (Floquet) many-body systems coupled to a dissipative bath, called open-system Floquet DMRG (OFDMRG). This method is based on a matrix product operator ansatz for the Floquet density matrix in frequency-space, and enables access to large systems beyond the reach of exact master-equation or quantum trajectory simulations, while retaining information about the periodic micro-motion in Floquet steady states. An excited-state extension of this technique also allows computation of t…
The universal critical behavior of the driven-dissipative non-equilibrium Bose-Einstein condensation transition is investigated employing the field-theoretical renormalization group method. Such criticality may be realized in broad ranges of driven open systems on the interface of quantum optics and many-body physics, from exciton-polariton condensates to cold atomic gases. The starting point is a noisy and dissipative Gross-Pitaevski equation corresponding to a complex valued Landau-Ginzburg functional, which captures the near critical non-equilibrium dynamics, and generalizes Model A for cla…
We show that short-range correlations have a dramatic impact on the steady-state phase diagram of quantum driven-dissipative systems. This effect, never observed in equilibrium, follows from the fact that ordering in the steady state is of dynamical origin, and is established only at very long times, whereas in thermodynamic equilibrium it arises from the properties of the (free) energy. To this end, by combining the cluster methods extensively used in equilibrium phase transitions to quantum trajectories and tensor-network techniques, we extend them to nonequilibrium phase transitions in diss…
Self-assembly, the process by which interacting components form well-defined and often intricate structures, is typically thought of as a spontaneous process arising from equilibrium dynamics. When a system is driven by external \emph{nonequilibrium} forces, states statistically inaccessible to the equilibrium dynamics can arise, a process sometimes termed direct self-assembly. However, if we fix a given target state and a set of external control variables, it is not well-understood i) how to design a protocol to drive the system towards the desired state nor ii) the energetic cost of persiste…
