Related papers: A dynamical-system picture of a simple branching-p…
We study an open system composed of two parallel totally asymmetric simple exclusion processes with particle attachment and detachment in the bulk. The particles are allowed to change their lane from lane-A to lane-B, but not conversely. We…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walks are proving to be effective simulators of such phenomena. Here we report the realization of a…
In this paper mathematical models for the evolutionary conserved Notch-Delta pathway are developed and analyzed in order to better understand how two neighboring biological cells can become different. We pursue a structure-based…
Granular systems confined in vertically vibrated shallow horizontal boxes (quasi two-dimensional geometry) present a liquid to solid phase transition when the frequency of the periodic forcing is increased. An effective model, where grains…
Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the…
Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior…
The continuous phase transition, indicated by the macroscopic order parameter and the occurrence of the spontaneous symmetry breaking, is well illustrated based on the Ginzburg-Landau's paradigm. In systems described by one order parameter,…
In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The…
Phase transitions are the macroscopic manifestation of microscopic processes that drive a system towards a new state. The detailed evolution of these processes, particularly in abrupt phase transitions, are currently not fully understood.…
We consider diffusion processes x_{t} on the unit interval. Doob-transformation techniques consist of a selection of x_{t}-paths procedure. The law of the transformed process is the one of a branching diffusion system of particles, each…
The dynamics of the Brans-Dicke theory with a quadratic scalar field potential function and barotropic matter is investigated. The dynamical system methods are used to reveal complexity of dynamical evolution in homogeneous and isotropic…
Phase transitions are a fundamental concept in science describing diverse phenomena ranging from, e.g., the freezing of water to Bose-Einstein condensation. While the concept is well-established in equilibrium, similarly fundamental…
We give a development of the ODE method for the analysis of recursive algorithms described by a stochastic recursion. With variability modelled via an underlying Markov process, and under general assumptions, the following results are…
In this paper, we study weakly interacting diffusion processes on random graphs. Our main focus is on the properties of the mean-field limit and, in particular, on the nonuniqueness and bifurcation structure of stationary states. By…
We solve a simple model that supports a dynamic phase transition and show conditions for the existence of the transition. Using methods of large deviation theory we analytically compute the probability distribution for activity and entropy…
We study a Weiner process that is conditioned to pass through a finite set of points and consider the dynamics generated by iterating a sample path from this process. Using topological techniques we are able to characterize the global…
We develop a comprehensive theoretical biophysics model grounded in a path integral perspective and an m-sectorial open-system framework, to describe complex, damped viral phonon dynamics in resource limited and noise driven environments.…
A version of the second order phase transition theory, in which the Nernst theorem holds automatically, is proposed. The theory is constructed in terms of the order parameter and the (configurational) entropy. It faithfully reproduces the…
We consider networks made of parallel lanes along which particles hop according to driven diffusive dynamics. The particles also hop transversely from lane to lane, hence indirectly coupling their longitudinal dynamics. We present a general…