Related papers: Convergence to equilibrium in a class of interacti…
A conservative Feller evolution on continuous bounded functions is constructed from a weakly continuous, time-inhomogeneous transition function describing a pure jump process on a locally compact Polish space. The transition function is…
Empirical evidence suggesting that living systems might operate in the vicinity of critical points, at the borderline between order and disorder, has proliferated in recent years, with examples ranging from spontaneous brain activity to…
How do cellular automata behave in the limit of a very large number of cells? Is there a continuum limit with simple properties? We attack this problem by mapping certain classes of automata to quantum field theories for which powerful…
We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…
Cellular automata can show well known features of quantum mechanics, such as a linear rule according to which they evolve and which resembles a discretized version of the Schroedinger equation. This includes corresponding conservation laws.…
We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…
Ageing phenomena are observed in a large variety of dynamical systems exhibiting a slow relaxation from a non-equilibrium initial state. Ageing can be characterised in terms of the linear response R(t,s) at time t to a local perturbation at…
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 investigate the role of equilibrium methods and stress transfer range in describing the process of damage. We find that equilibrium approaches are not applicable to the description of damage and the catastrophic failure mechanism if the…
We determine the late-time dynamics of a generic spin ensemble with inhomogeneous broadening - equivalently, qubits with arbitrary Zeeman splittings - coupled to a dissipative environment with strength decreasing as $1/t$. The approach to…
We briefly review some equilibrium and nonequilibrium properties of systems with long-range interactions. Such systems, which are characterized by a potential that weakly decays at large distances, have striking properties at equilibrium,…
We study a far-from-equilibrium system of interacting particles, hopping between sites of a 1d lattice with a rate which increases with the number of particles at interacting sites. We find that clusters of particles, which initially…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
We investigate the impact of momentum-dependent relaxation time approximation in the Boltzmann equation within the Bjorken flow framework by analyzing the moments of the single-particle distribution function. The moment equations, which…
Metriplectic dynamical systems consist of a special combination of a Hamiltonian and a (generalized) entropy-gradient flow, such that the Hamiltonian is conserved and entropy is dissipated/produced (depending on a sign convention). It is…
Systems of identical particles possessing non-local interactions are capable of exhibiting extra-classical properties beyond the characteristic quantum length scales. This letter derives the dynamics of such systems in the non-relativistic…
We study the long-time behavior of the solutions of a two-component reaction-diffusion system on the real line, which describes the basic chemical reaction $A <=> 2 B$. Assuming that the initial densities of the species $A, B$ are bounded…
We consider percolation and jamming transitions for particulate systems exposed to compression. For the systems built of particles interacting by purely repulsive forces in addition to friction and viscous damping, it is found that these…
We consider two models of deterministic active particles in an external potential. In the limit where the speed of a particle is fixed, both models coincide and can be formulated as a Hamiltonian system, but only if the potential is…
We demonstrate the emergence of self-organized structures in the course of the relaxation of an initially excited, dissipative and finite chain of interacting particles in a periodic potential towards its many particle equilibrium…