We study the carrier concentration bistabilities that occur to a highly photo-excited electron gas. The kinetics of this non-equilibrium electron gas is given by a set of nonlinear rate equations. For low temperatures and cw photo-excitation we show that they have three steady state solutions when the photo-excitation energy is in a certain interval which depends on the electron-electron interaction. Two of them are stable and the other is unstable. We also find the hysteresis region in terms of which these bistabilities are expressed. A diffusion model is constructed which allows the coexistence of two homogeneous spatially separated phases in the non-equilibrium electron gas. The order parameter is the difference of the electron population in the bottom of the conduction band of these two steady stable states. By defining a generalized free potential we obtain the Maxwell construction that determines the order parameter. This order parameter goes to zero when we approach to the critical curve. Hence, this phase transition is a non-equilibrium first order phase transition.
The evolutionary effect of recombination depends crucially on the epistatic interactions between linked loci. A paradigmatic case where recombination is known to be strongly disadvantageous is a two-locus fitness landscape dis- playing reciprocal sign epistasis with two fitness peaks of unequal height. Focusing on the occurrence of bistability in the equilibrium solutions, we consider here the deterministic, haploid two-locus model with reversible mu- tations, selection and recombination. We find analytic formulae for the criti- cal recombination probability rc above which two stable stationar…
A prototype model of a stochastic one-variable system with a linear restoring force driven by two cross-correlated multiplicative and additive Gaussian white noises was considered earlier [S. I. Denisov et al., Phys. Rev. E 68, 046132 (2003)]. The multiplicative factor was assumed to be quadratic in the vicinity of a stable equilibrium point. It was determined that a negative cross-correlation can induce nonequilibrium transitions. In this paper, we investigate this model in more detail and calculate explicit expressions of the stationary probability density. We construct a phase diagram and s…
We explore fluctuation relations in a periodically driven micromechanical torsional oscillator. In the linear regime where the modulation is weak, we verify that the ratio of the work variance to the mean work is constant, consistent with conventional fluctuation theorems. We then increase the amplitude of the periodic drive so that the response becomes nonlinear and two nonequilibrium oscillation states coexist. Due to interstate transitions, the work variance exhibits a peak at the driving frequency at which the occupation of the two states is equal. Moreover, the work fluctuations depend ex…
Stochastic processes govern the time evolution of a huge variety of realistic systems throughout the sciences. A minimal description of noisy many-particle systems within a Markovian picture and with a notion of spatial dimension is given by probabilistic cellular automata, which typically feature time-independent and short-ranged update rules. Here, we propose a simple cellular automaton with power-law interactions that gives rise to a bistable phase of long-ranged directed percolation whose long-time behaviour is not only dictated by the system dynamics, but also by the initial conditions. I…
We reply the comment made by Caracciolo et al. (cond. mat./0305213) to our work "Dynamic behavior of anisotropic non-equilibrium driving lattice gases", cond-mat/021041.
We derive the exact formula for thermal-equilibrium spacing distribution of one-dimensional particle gas with repulsive potential depending on the distance r between the neighboring particles. We are focused on the power-law potentials r^(-a) for a>0, being motivated by the actual traffic research.
One particle in a classical perfect gas is driven out of equilibrium by changing its mass over a short time interval. The work done on the driven particle depends on its collisions with the other particles in the gas. This model thus provides an example of a non-equilibrium process in a system (the driven particle) coupled to an environment (the rest of the gas). We calculate the work done on the driven particle and compare the results to Jarzynski's equality relating a non-equilibrium work process to an equilibrium free-energy difference. The results for this model are generalised to the case…
It is shown that the partial temperatures of a homogeneous multicomponent gas mixture in the thermodynamical equilibrium cannot be equal to each other. New general solutions for equilibrium distribution functions of the multicomponent mixture are found. Parameters (including partial temperatures) involved in these solutions are determined by means of physical conditions which follow from a notion of the stable thermodynamical equilibrium. The found relations of the partial temperatures to the mean mixture temperature are dependent on the molecular weights and concentrations of the components. …
We employ Monte Carlo simulations to study the non-equilibrium relaxation of driven Ising lattice gases in two dimensions. Whereas the temporal scaling of the density auto-correlation function in the non-equilibrium steady state does not allow a precise measurement of the critical exponents, these can be accurately determined from the aging scaling of the two-time auto-correlations and the order parameter evolution following a quench to the critical point. We obtain excellent agreement with renormalization group predictions based on the standard Langevin representation of driven Ising lattice …
We consider a heavy piston in an infinite cylinder surrounded by ideal gases on both sides. The piston moves under elastic collisions with gas atoms. We assume here that the gases always exert equal pressures on the piston, hence the piston remains at the so called mechanical equilibrium. However, the temperatures and densities of the gases may differ across the piston. In that case some earlier studies by Gruber, Piasecki and others reveal a very slow motion (drift) of the piston in the direction of the hotter gas. At the same time the hotter gas slowly transfers its energy (heat) across the …
We present a thermodynamic formulation for scale-invariant systems based on the principle of extreme information. We create an analogy between these systems and the well-known thermodynamics of gases and fluids, and study as a compelling case the non-interacting system -the scale-free ideal gas- presenting some empirical evidences of electoral results, city population and total cites of Physics journals that confirm its existence. The empirical class of universality known as Zipf's law is derived from first principles: we show that this special class of power law can be understood as the densi…
The non-equilibrium thermodynamics of a gas inside a piston is a conceptually simple problem where analytic results are rare. For example, it is hard to find in the literature analytic formulas that describe the heat exchanged with the reservoir when the system either relaxes to equilibrium or is compressed over a finite time. In this paper we derive such kind of analytic formulas. To achieve this result, we take the equations derived by Cerino \textit{et al.} [Phys. Rev. E \textbf{91}, 032128] describing the dynamic evolution of a gas-piston system, we cast them in a dimensionless form and we…
Gibbs' phase rule states that two-phase coexistence of a single-component system, characterized by an n-dimensional parameter-space, may occur in an n-1-dimensional region. For example, the two equilibrium phases of the Ising model coexist on a line in the temperature-magnetic-field phase diagram. Nonequilibrium systems may violate this rule and several models, where phase coexistence occurs over a finite (n-dimensional) region of the parameter space, have been reported. The first example of this behaviour was found in Toom's model [Toom,Geoff,GG], that exhibits generic bistability, i.e. two-p…
The concentration-dependent switching of the non-equilibrium depletion forces between obstacles in an interacting Brownian gas flow is presented. It is shown that this switching is caused by the blockade effect for the gas particles. With increasing equilibrium gas concentration, the gas particles blockade causes the obstacle wake inversion (trace profile turn-over) that, in turn, leads to the change of sign of dissipative interaction. Some non-linear effects such as formation of a cavity-like sparse wake behind the obstacle and the dissipative pairing effect are discussed briefly. The results…
A kinetic equation for a dilute gas of hard spheres confined between two parallel plates separated a distance smaller than two particle dimeters is derived. It is a Boltzmann-like equation, which incorporates the effect of the confinement on the particle collisions. A function $S(t)$ is constructed by adding to the Boltzmann expression a confinement contribution. Then it is shown that for the solutions of the kinetic equation, $S(t)$ increases monotonically in time, until the system reaches a stationary inhomogeneous state, when $S$ becomes the equilibrium entropy of the confined system as der…
Northumbria University（诺森比亚大学）；The Open University（开放大学）；Boston University（波士顿大学）；Santa Fe Institute（圣塔菲研究所）；Institute of Problems in Mechanical Engineering, Russian Academy of Sciences（俄罗斯科学院机械问题研究所）
Examination of equilibrium radiation in plasma media shows that the spectral the energy distribution of such radiation is different from the Planck equilibrium radiation. Using the previously obtained general relations for the spectral energy density of equilibrium radiation in a system of charged particles, we consider radiation in an electron in the limiting case of an infinitesimal damping. It is shown that zero vacuum fluctuations which are part of the full spectral energy distribution should be renormalized. In this case, the renormalized zero vacuum fluctuations depend on the electron de…
The quasi-stationary nonequilibrium distribution function of an independent electron gas interacting with a medium, which is at local thermal equilibrium, can be obtained by entropy production rate minimization, subject to constraints of fixed moments. The result is not restricted to the region near equilibrium (linear response) and provides a closure of the associated generalized hydrodynamic equations of the electron gas for an arbitrary number of moments. Besides an access to far from equilibrium states, the approach provides a useful description of semi-classical transport in mesoscopic co…
The maximum complexity momentum distribution for an isolated monodimensional ideal gas out of equilibrium is derived analytically. In a first approximation, it consists of a double non-overlapping Gaussian distribution. In good agreement with this result, the numerical simulations of a particular isolated monodimensional gas, which is abruptly pushed far from equilibrium, shows the maximum complexity distribution in the decay of the system toward equilibrium.
We use computer simulation to study the layer-by-layer growth of particle structures in a lattice gas, taking the number of incorporated vacancies as a measure of the quality of the grown structure. By exploiting a dynamic scaling relation between structure quality in and out of equilibrium, we determine that the best quality of structure is obtained, for fixed observation time, with strong interactions and far-from-equilibrium growth conditions. This result contrasts with the usual assumption that weak interactions and mild nonequilibrium conditions are the best way to minimize errors during …
We derive the exact formula for thermal-equilibrium spacing distribution of one-dimensional particle gas with repulsive potential V(r)=r^(-a) (a>0) depending on the distance r between the neighboring particles. The calculated distribution (for a=1) is successfully compared with the highway-traffic clearance distributions, which provides a detailed view of changes in microscopical structure of traffic sample depending on traffic density. In addition to that, the observed correspondence is a strong support of studies applying the equilibrium statistical physics to traffic modelling.
An operator that governs the discrete time evolution of the velocity distribution of an out-of-equilibrium ideal gas will be presented. This nonlinear map, which conserves the momentum and the energy of the ideal gas, has the Maxwellian Velocity Distribution (MVD) as an asymptotic equilibrium. Moreover, the system displays the increasing of the entropy during the decay to the MVD.
We obtain the equations that define the equilibrium of a homogeneous relativistic gas of neutrons, protons and electrons in a constant magnetic field as applied to the conditions that probably occur near the center of neutron stars. We compute the relative densities of the particles at equilibrium and the Fermi momentum of electrons in the strong magnetic field as function of the density of neutrons and the magnetic field induction. Novel features are revealed as to the ratio of the number of protons to the number of neutrons at equilibrium in the presence of large magnetic fields.
A simple 1D lattice gas model is presented, which very well describes the equilibrium and kinetic behaviors of water confined in a thin carbon nanotube found in an atomistic molecular dynamics(MD) simulation {[} Nature {\bf 414}, 188 (2001) {]}. The model parameters are corresponding to various physical interactions and can be calculated or estimated in statistic mechanics. The roles of every interaction in the water filling, emptying and transporting processes are clearly understood. Our results indicate that the physical picture of the single-file kinetics is very simple.
The dependence of the three lowest order spatial correlation functions of a harmonically confined Bose gas on temperature and interaction strength is presented at equilibrium. Our analysis is based on a stochastic Langevin equation for the order parameter of a weakly-interacting gas. Comparison of the predicted first order correlation functions to those of appropriate mean field theories demonstrates the potentially crucial role of density fluctuations on the equilibrium coherence length. Furthermore,the change in both coherence length and shape of the correlation function, from gaussian to ex…
Integer lattice gas automata can be utilized as building blocks in statistical mechanics. The presented deterministic and reversible automaton generates semiclassical statistical distributions. A possible approach to Bose-Einstein statistics from cellular automata position is discussed.
Recently, new results on percolation of interdependent networks have shown that the percolation transition can be first order. In this paper we show that, when considering antagonistic interactions between interacting networks, the percolation process might present a bistability of the equilibrium solution. To this end, we introduce antagonistic interactions for which the functionality, or activity, of a node in a network is incompatible with the functionality, of the linked nodes in the other interacting networks. In particular, we study the percolation transition in two interacting networks …
Nonequilibrium dynamics of an N-fold spin-degenerate ultracold Fermi gas is described in terms of beyond-mean-field Kadanoff-Baym equations for correlation functions. Using a nonperturbative expansion in powers of 1/N, the equations are derived from the two-particle irreducible effective action in Schwinger-Keldysh formulation. The definition of the nonperturbative approximation on the level of the effective action ensures vital conservation laws as, e.g., for the total energy and particle number. As an example, the long-time evolution of a homogeneous, twofold spin-degenerate Fermi gas is stu…
Intrinsic stochasticity can induce highly non-trivial effects on dynamical systems, including stochastic and coherence resonance, noise induced bistability, noise-induced oscillations, to name but a few. In this paper we revisit a mechanism first investigated in the context of neuroscience by which relatively small demographic (intrinsic) fluctuations can lead to the emergence of avalanching behavior in systems that are deterministically characterized by a single stable fixed point (up state). The anomalously large response of such systems to stochasticity stems (or is strongly associated with…
The received wisdom in statistical mechanics is that isolated systems, when left to themselves, approach equilibrium. But under what circumstances does an equilibrium state exist and an approach to equilibrium take place? In this paper we address these questions from the vantage point of the long-run fraction of time definition of Boltzmannian equilibrium that we developed in two recent papers (Werndl and Frigg 2015a, 2015b). After a short summary of Boltzmannian statistical mechanics and our definition of equilibrium, we state an existence theorem which provides general criteria for the exist…
We present a review of recent work on the statistical mechanics of non equilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and can be studied rigorously providing a source of challenging mathematical problems. In this way, some principles of wide validity have been obtained leading to interesting physical consequences.
