Related papers: Hydrostatics and dynamical large deviations for a …
We consider some interacting particle processes with long-range dynamics: the zero-range and exclusion processes with long jumps. We prove that the hydrodynamic limit of these processes corresponds to a (possibly non-linear) fractional heat…
Using duality techniques, we derive the hydrodynamic limit for one-dimensional, boundary-driven, symmetric exclusion processes with different types of non-reversible dynamics at the boundary, for which the classical entropy method fails.
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
We provide a compact derivation of the static and dynamic equations for infinite-dimensional particle systems in the liquid and glass phases. The static derivation is based on the introduction of an "auxiliary" disorder and the use of the…
We study the hydrodynamic behaviour of the asymmetric simple exclusion process on the lattice of size $n$. In the bulk, the exclusion dynamics performs rightward flux. At the boundaries, the dynamics is attached to reservoirs. We…
We prove the hydrodynamic limit for a one dimensional harmonic chain with a random flip of the momentum sign. The system is open and subject to two thermostats at the boundaries and to an external tension at one of the endpoints. Under a…
We derive the hydrodynamic limit of a kinetic equation where the interactions in velocity are modelled by a linear operator (Fokker-Planck or Linear Boltzmann) and the force in the Vlasov term is a stochastic process with high amplitude and…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
We obtain large deviation results for a two time-scale model of jump-diffusion processes. The processes on the two time scales are fully inter-dependent, the slow process has small perturbative noise and the fast process is ergodic. Our…
We derive hydrodynamics of a prototypical one dimensional model, having variable-range hopping, which mimics passive diffusion and ballistic motion of active, or self-propelled, particles. The model has two main ingredients - the hardcore…
We extend the usual hydrodynamic description of the symmetric exclusion process by keeping track of collision events corresponding to jumps into already occupied sites, thereby quantifying the dissipated part of the microscopic activity…
We revisit in this short article the hydrostatic limit for the exclusion process with slow boundary. The original proof of this result relies on estimates of the correlation functions. We achieve the same result based on analysis of two…
We investigate the hydrodynamic behavior and local equilibrium of the multilane exclusion process, whose invariant measures were studied in our previous paper \cite{mlt1a}. The dynamics on each lane follows a hyperbolic time scaling,…
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…
We formulate a relativistic hydrodynamic theory for fluids with spin and intrinsic dilation charges. Using an entropy-current analysis, we derive constitutive relations featuring a bulk viscosity and a dilation conductivity governing the…
In hydrodynamical modelling of ultrarelativistic heavy-ion collisions the freeze-out is typically assumed to take place on a surface of constant temperature or energy density. In this work we apply a dynamical freeze-out criterion, which…
In the course of Darwinian evolution of a population, punctualism is an important phenomenon whereby long periods of genetic stasis alternate with short periods of rapid evolutionary change. This paper provides a mathematical interpretation…
Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally. Our analysis reveals three distinct…
Using the large-deviation formalism, we study the statistics of current fluctuations in a diffusive nonequilibrium quantum spin chain. The boundary-driven XX chain with dephasing consists of a coherent bulk hopping and a local dissipative…
We consider attractive particle systems in $\Z^d$ with product invariant measures. We prove that when particles are restricted to a subset of $\Z^d$, with birth and death dynamics at the boundaries, the hydrodynamic limit is given by the…