Diffusion and Relaxation Controlled by Tempered α-stable Processes
Authors: Aleksander Stanislavsky, Karina Weron, Aleksander Weron
Abstract
We derive general properties of anomalous diffusion and nonexponential relaxation from the theory of tempered \alpha-stable processes. Its most important application is to overcome the infinite-moment difficulty for the \alpha-stable random operational time \tau. The tempering results in the existence of all moments of \tau. The subordination by the inverse tempered \alpha-stable process provides diffusion(relaxation) that occupies an intermediate place between subdiffusion (Cole-Cole law) and normal diffusion (exponential law). Here we obtain explicitly the Fokker-Planck equation, the mean square displacement and the relaxation function. This model includes subdiffusion as a particular case.
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Abstract
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Abstract
We show that macroscopic irreversible thermodynamics for viscous fluids can be derived from exact information-theoretic thermodynamic identities valid at the microscale. Entropy production in particular is a measure of the loss of many-particle correlations in the same way in which it measures the loss of system-reservoirs correlations in stochastic thermodynamics (ST). More specifically, we first show that boundary conditions at the macroscopic level define a natural decomposition of the entropy production rate (EPR) in terms of thermodynamic forces multiplying their conjugated currents, as well as a change in suitable nonequilibrium potential that acts as a Lyapunov function in absence of …
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Continuously varying exponents in the distribution of waiting times in the symmetric exclusion process on a percolation clusterArpan Chatterjee, Kabir Ramola, Deepak Dhar · 2026 · Statistical Mechanics · Not summarized yet
Abstract
We study the waiting-time distribution of hard-core interacting particles in the symmetric exclusion process on one- and two-dimensional lattices with side branches attached to each lattice site in the steady state. We use numerical simulations together with an approximate analytical treatment of particles trapped in side branches in the steady state. Such a two-dimensional carpet serves as a simplified model for trapping of a supercritical percolation cluster. At high particle densities, the system exhibits strong dynamical heterogeneity, with the distribution of logarithms of waiting times developing well-separated peaks corresponding to particles trapped at different depths from the backb…
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Large deviation functional of the weakly asymmetric exclusion processB. Derrida, C. Enaud · 2003 · J. Stat. Phys. 114 (2004) 537-562 · AI summary available
Abstract
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Abstract
Few analytical methods exist for quantitative studies of large fluctuations in stochastic systems. In this article, we develop a simple diagrammatic approach to the Chemical Master Equation that allows us to calculate multi-time correlation functions which are accurate to a any desired order in van Kampen's system size expansion. Specifically, we present a set of Feynman rules from which this diagrammatic perturbation expansion can be constructed algorithmically. We then apply the methodology to derive in closed form the leading order corrections to the linear noise approximation of the intrinsic noise power spectrum for general biochemical reaction networks. Finally, we illustrate our resul…
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Abstract
Non-equilibrium dynamics are present in many aspects of our lives, ranging from microscopic physical systems to the functioning of the brain. What characterizes stochastic models of non-equilibrium processes is the breaking of the fluctuation-dissipation relations as well as the existence of non-static stable states, or phases. A prototypical example is a dynamical phase characterized by a limit cycle - the order parameter of finite magnitude rotating or oscillating at a fixed frequency. Consequently, birhythmicity, where two stable limit cycles coexist, is a natural extension of the simpler single limit cycle phase. Both the abundance of real systems exhibiting such states as well as their …
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Abstract
Power-law distributions are ubiquitous in nature. Random multiplicative processes are a basic model for the generation of power-law distributions. It is known that, for discrete-time systems, the power-law exponent decreases as the autocorrelation time of the multiplier increases. However, for continuous-time ystems, it has not yet been elucidated as to how the temporal correlation affects the power-law behavior. Herein, we have analytically investigated a multiplicative Langevin equation with colored noise. We show that the power-law exponent depends on the details of the multiplicative noise, in contrast to the case of discrete-time systems.
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Abstract
The state of an open quantum system undergoing an adiabatic process evolves by following the instantaneous stationary state of its time-dependent generator. This observation allows one to characterize, for a generic adiabatic evolution, the average dynamics of the open system. However, information about fluctuations of dynamical observables, such as the number of photons emitted or the time-integrated stochastic entropy production in single experimental runs, requires controlling the whole spectrum of the generator and not only the stationary state. Here, we show how such information can be obtained in adiabatic open quantum dynamics by exploiting tools from large deviation theory. We prove …
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