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We review recent results on an exactly solvable model of nonequilibrium statistical mechanics, specifically the classical Rule 54 reversible cellular automaton and some of its quantum extensions. We discuss the exact microscopic description…
We propose and discuss two variants of kinetic particle models - cellular automata in 1+1 dimensions, which have some appeal due to their simplicity and intriguing properties which could warrant further research and applications. The first…
Recently Prosen and Mej\'ia-Monasterio (J. Phys. A: Math. Theor. 49 (2016) 185003) obtained exact nonequilibrium steady states of an integrable and reversible cellular automaton driven by some stochastic boundary conditions. In this paper,…
We introduce a pair of time-reversible models defined on the discrete space-time lattice with 3 states per site, specifically, a vacancy and a particle of two flavours (species). The local update rules reproduce the rule 54 reversible…
We analyze a stochastic 5-neighbor cellular automaton with several conserved quantities, including the particle density. By examining the eigenvalue problem of the associated transition matrix, we derive an explicit formula for the…
In this paper we study the space evolution in the Rule 54 reversible cellular automaton, which is a paradigmatic example of a deterministic interacting lattice gas. We show that the spatial translation of time configurations of the…
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…
We study two common types of time-noncontinuous updates for one dimensional stochastic cellular automata with arbitrary nearest neighbor interactions and arbitrary open boundary conditions. We first construct the stationary states using the…
We discuss various properties of Probabilistic Cellular Automata, such as the structure of the set of stationary measures and multiplicity of stationary measures (or phase transition) for reversible models.
We study integrability properties of a reversible deterministic cellular automaton (the rule 54 of [Bobenko et al., Commun. Math. Phys. 158, 127 (1993)]) and present a bulk algebraic relation and its inhomogeneous extension which allow for…
We present an explicit time-dependent matrix product ansatz (tMPA) which describes the time-evolution of any local observable in an interacting and deterministic lattice gas, specifically for the rule 54 reversible cellular automaton of…
We study the statistical properties of the long-time dynamics of the rule 54 reversible cellular automaton (CA), driven stochastically at its boundaries. This CA can be considered as a discrete-time and deterministic version of the…
We study metastability and mixing time for a non-reversible probabilistic cellular automaton. With a suitable choice of the parameters, we first show that the stationary distribution is close in total variation to a low temperature Ising…
In this paper, we propose a stochastic cellular automaton model of traffic flow extending two exactly solvable stochastic models, i.e., the asymmetric simple exclusion process and the zero range process. Moreover it is regarded as a…
The transport and chemical reactions of solutes are modelled as a cellular automaton in which molecules of different species perform a random walk on a regular lattice and react according to a local probabilistic rule. The model describes…
In a recent paper [arXiv:1506.06649 [nlin.CG]], we presented an example of a 3-state cellular automaton which exhibits behaviour analogous to degenerate hyperbolicity often observed in finite-dimensional dynamical systems. We also…
In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over…
We focus on a family of one-dimensional probabilistic cellular automata with memory two: the dynamics is such that the value of a given cell at time $t+1$ is drawn according to a distribution which is a function of the states of its two…
We study the dynamics of the Rule 150 reversible cellular automaton (RCA). This is a one-dimensional lattice system of binary variables with synchronous (Floquet) dynamics, corresponding to a bulk deterministic and reversible discrete…
For an interacting spatio-temporal lattice system we introduce a formal way of expressing multi-time correlation functions of local observables located at the same spatial point with a time state, i.e. a statistical distribution of…