相关论文: The Steady State Distribution of the Master Equati…

We prove that the steady state of a class of multidimensional reaction-diffusion systems is asymptotically stable at the intersection of unweighted space and exponentially weighted Sobolev spaces, and pay particular attention to a special…

Some general aspects of nonlinear transport phenomena are discussed on the basis of two kinds of formulations obtained by extending Kubo's perturbational scheme of the density matrix and Zubarev's non-equilibrium statistical operator…

The local approach to construct master equation for a composite open system with a weak internal coupling is simple and seems reasonable. However, it is thermodynamic consistent only when the subsystems are resonantly coupled. Efforts are…

Due to the existence of multiple stationary distributions, we study the stability and instability of a stationary distribution for distribution dependent stochastic differential equations. This note is devoted to the instability of a…

We consider an n-player symmetric stochastic game with weak interaction between the players. Time is continuous and the horizon and the number of states are finite. We show that the value function of each of the players can be approximated…

We present a direct parametrization for continuous-time stochastic state-space models that ensures external stability via the stochastic bounded-real lemma. Our formulation facilitates the construction of probabilistic priors that enforce…

In the framework of theory of open quantum systems, we derive quantum master equations for the ultrastrong system-bath coupling regime and, more generally, the strong-decoherence regime. In this regime, the strong decoherence is…

We consider two two-level atoms fixed at different positions, driven by a monochromatic laser field, and interacting collectively with the vacuum electromagnetic field. A Born-Markov-secular master equation is used to describe the dynamics…

We consider Mc Kean-Vlasov stochastic differential equations (MVSDEs), which are SDEs where the drift and diffusion coefficients depend not only on the state of the unknown process but also on its probability distribution. This type of SDEs…

We investigate the class of tempered stable distributions and their associated processes. Our analysis of tempered stable distributions includes limit distributions, parameter estimation and the study of their densities. Regarding tempered…

Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…

In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…

We study steady-state properties of inelastic gases in two-dimensions in the presence of an energy source. We generalize previous hydrodynamic treatments to situations where high and low density regions coexist. The theoretical predictions…

To obtain further insight on possible power law generalizations of Boltzmann equilibrium concepts, a stochastic collision model is investigated. We consider the dynamics of a tracer particle of mass $M$, undergoing elastic collisions with…

The master equation plays an important role in many scientific fields including physics, chemistry, systems biology, physical finance, and sociodynamics. We consider the master equation with periodic transition rates. This may represent an…

The kinetic wave equation arises in wave turbulence to describe the Fourier spectrum of solutions to the cubic Schroedinger equation. The equation has two Kolmogorov-Zakharov steady states corresponding to out-of-equilibrium cascades…

Master equation could be applied to model various kinds of biochemical systems. A general theory for its time-dependent nonequilibrium thermodynamics is rigorously derived. We not only introduce a concept of general internal energy, but…

The existence of stationary distributions to distribution dependent stochastic differential equations are investigated by using the ergodicity of the associated decoupled equation and the Schauder fixed point theorem. By using Zvonkin's…

The nonequilibrium steady state of an infinite-range Ising model is studied. The steady state is obtained by dividing the spins into two groups and attaching them to two heat baths generating spin flips at different temperatures. In the…

The non-equilibrium statistical mechanics and kinetic theory for a model of a confined quasi-two-dimensional gas of inelastic hard spheres is presented. The dynamics of the particles includes an effective mechanism to transfer the energy…