Related papers: Factorised steady states for multi-species mass tr…
We provide a generic scheme to separate the particles of a mixture by their physical properties like mass, friction or size. The scheme employs a periodically shaken two dimensional dissipative lattice and hinges on a simultaneous transport…
Continuous-time random walks combining diffusive scattering and ballistic propagation on lattices model a class of L\'evy walks. The assumption that transitions in the scattering phase occur with exponentially-distributed waiting times…
We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…
By considering the master equation of the partially asymmetric diffusion process on a one-dimensional lattice, the most general boundary condition (i.e. interactions) for the multi-species reaction-diffusion processes is considered.…
Kinetic constraints are generally expected to slow down dynamics in many-body systems, obstructing or even completely suppressing transport of conserved charges. Here, we show how gauge theories can defy this wisdom by yielding constrained…
At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…
Finite dynamical systems (FDSs) are commonly used to model systems with a finite number of states that evolve deterministically and at discrete time steps. Considered up to isomorphism, those correspond to functional graphs. As such, FDSs…
By considering the master equation of asymmetric exclusion process on a one-dimensional lattice, we obtain the most general boundary condition of the multi-species exclusion processes in which the number of particles is constant in time.…
This paper introduces factored conditional filters, new filtering algorithms for simultaneously tracking states and estimating parameters in high-dimensional state spaces. The conditional nature of the algorithms is used to estimate…
A rather simple random walk model on a one-dimensional lattice is put forward. The lattice as a whole switches randomly between two possible states which are spatially symmetric. Both lattice states are identical, but translated by one site…
We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be…
When modelling driven steady states of matter, it is common practice either to choose transition rates arbitrarily, or to assume that the principle of detailed balance remains valid away from equilibrium. Neither of those practices is…
We study the phenomenon of real space condensation in the steady state of a class of mass transport models where the steady state factorises. The grand canonical ensemble may be used to derive the criterion for the occurrence of a…
The Quasi Steady-State (QSS) model of long-term dynamics relies on the idea of time-scale decomposition. Assuming that the fast variables are infinitely fast and are stable in the long-term, the QSS model replaces the differential equations…
It was recently suggested by Blythe and Evans that a properly defined steady state normalisation factor can be seen as a partition function of a fictitious statistical ensemble in which the transition rates of the stochastic process play…
We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
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…
This paper derives distributed conditions that guarantee the system-wide stability for power systems with nonlinear and heterogeneous bus dynamics interconnected via power network. Our conditions require each bus dynamics should satisfy…
A macroscopic theory for describing cellular states during steady-growth is presented, which is based on the consistency between cellular growth and molecular replication, as well as the robustness of phenotypes against perturbations.…