Related papers: Integrable Floquet dynamics, generalized exclusion…
We study a one-parameter generalization of the symmetric simple exclusion process on a one dimensional lattice. In addition to the usual dynamics (where particles can hop with equal rates to the left or to the right with an exclusion…
The Finite Element Method (FEM) is the gold standard for spatial discretization in numerical simulations for a wide spectrum of real-world engineering problems. Prototypical areas of interest include linear heat transfer and linear…
This paper introduces a comprehensive extension of the path integral formalism to model stochastic processes with arbitrary multiplicative noise. To do so, It\^o diffusive process is generalized by incorporating a multiplicative noise term…
In this paper it is shown that the steady-state weights of the asymmetric simple exclusion process (ASEP) with open boundaries and parallel update can be written as a product of a scalar pair-factorized and a matrix-product state. This type…
We present a numerical approach to calculate non-equilibrium eigenstates of a periodically time-modulated quantum system. The approach is based on the use of a chain of single-step time-independent propagating operators. Each operator is…
In this paper, we propose a compositional approach for the construction of finite abstractions (a.k.a. finite Markov decision processes (MDPs)) for networks of discrete-time stochastic control subsystems that are not necessarily…
Many physical, biological or social systems are governed by history-dependent dynamics or are composed of strongly interacting units, showing an extreme diversity of microscopic behaviour. Macroscopically, however, they can be efficiently…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
The space-time dynamics of rigid inhomogeneities (inclusions) free to move in a randomly fluctuating fluid bio-membrane is derived and numerically simulated as a function of the membrane shape changes. Both vertically placed (embedded)…
Computing the stochastic entropy production associated with the evolution of a stochastic dynamical system is a well-established problem. In a small number of cases such as the Ornstein-Uhlenbeck process, of which we give a complete…
Dynamical phase transitions are crucial features of the fluctuations of statistical systems, corresponding to boundaries between qualitatively different mechanisms of maintaining unlikely values of dynamical observables over long periods of…
Modelling the evolution of a system using stochastic dynamics typically implies a greater subjective uncertainty in the adopted system coordinates as time progresses, and stochastic entropy production has been developed as a measure of this…
In Floquet engineering, periodic driving is used to realize novel phases of matter which are inaccessible in thermal equilibrium. For this purpose, the Floquet theory provides us a recipe of obtaining a static effective Hamiltonian.…
The totally asymmetric simple exclusion process with generalized update is a version of the discrete time totally asymmetric exclusion process with an additional inter-particle interaction that controls the degree of particle clustering.…
The stochastic entropy generated during the evolution of a system interacting with an environment may be separated into three components, but only two of these have a non-negative mean. The third component of entropy production is…
We present a theoretical investigation of the stochastic dynamics of a damped particle in a tilted periodic potential with a double well per period. By applying the matrix continued fraction technique to the Fokker-Planck equation in…
Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary…
A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo and Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N stochastic variables with Lochner's generalized Dirichlet distribution (R.H. Lochner, A Generalized…