Related papers: Generalized Langevin equation with fluctuating dif…
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…
We presented a general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and Zubarev's nonequilibrium…
Within the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard…
We present a short overview of the recent results in the theory of diffusion and wave equations with generalised derivative operators. We give generic examples of such generalised diffusion and wave equations, which include time-fractional,…
Wang et al. [PNAS 106 (2009) 15160] have found that in several systems the linear time dependence of the mean-square displacement (MSD) of diffusing colloidal particles, typical of normal diffusion, is accompanied by a non-Gaussian…
The irreversible generalized Langevin equation (iGLE) contains a nonstationary friction kernel that in certain limits reduces to the GLE with space-dependent friction. For more general forms of the friction kernel, the iGLE was previously…
We present Generalized Contrastive Divergence (GCD), a novel objective function for training an energy-based model (EBM) and a sampler simultaneously. GCD generalizes Contrastive Divergence (Hinton, 2002), a celebrated algorithm for…
A wide class of nonlinear Langevin equations with drift and diffusion coefficients separable in time and space driven by the Gaussian white noise is analyzed in terms of a generalized n-moment. We show the system may present ergodic…
The fluctuation-dissipation theorem is a central result in statistical mechanics and is usually formulated for systems described by diffusion processes. In this paper, we propose a generalization for a wider class of stochastic processes,…
Fluctuations associated with relaxations in far-from-equilibrium regime is of fundamental interest for a large variety of systems within broad scales. Recent advances in techniques such as spectroscopy have generated the possibility for…
An analogy is drawn between the diffusion-wave equations derived from the fractional Kelvin-Voigt model and those obtained from Buckingham's grain-shearing (GS) model [J. Acoust. Soc. Am. 108, 2796-2815 (2000)] of wave propagation in…
The potential of mean force (PMF) is an effective average potential acting on an open system, renormalized due to the interaction with the surrounding thermal bath. The PMF determines the correction to the equilibrium Gibbs distribution,…
We study the effects of diffusion on a $\Lambda$-gradient echo memory, which is a coherent optical quantum memory using thermal gases. The efficiency of this memory is high for short storage time, but decreases exponentially due to…
We recently showed that the dynamics of coarse-grained observables in systems out of thermal equilibrium are governed by the non-stationary generalized Langevin equation [J. Chem. Phys. 147, 214110 (2017), J. Chem. Phys. 150, 174118…
Fundamental understanding of complex dynamics in many-particle systems on the atomistic level is of utmost importance. Often the systems of interest are of macroscopic size but can be partitioned into few important degrees of freedom which…
We consider the effects of long-range temporal correlations in many-particle systems, focusing particularly on fluctuations about the typical behaviour. For a specific class of memory dependence we discuss the modification of the large…
In this paper, a higher order finite difference scheme is proposed for Generalized Fractional Diffusion Equations (GFDEs). The fractional diffusion equation is considered in terms of the generalized fractional derivatives (GFDs) which uses…
Fluctuation-Dissipation Relations (FDR) for a Maxwell fluid are computed via the GENERIC formalism. This formalism is determined by four building blocks, two ``potentials'' (total energy and entropy) and two ``matrices'' which determine the…
We introduce a general formulation of the fluctuation-dissipation relations (FDR) holding also in far-from-equilibrium stochastic dynamics. A great advantage of this version of the FDR is that it does not require the explicit knowledge of…
Strong interaction with other particles or feedback from the medium on a Brownian particle entail memory effects in the effective dynamics. We discuss the extension of the fluctuation-dissipation theorem to nonequilibrium Langevin systems…