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Many interesting phenomena in nature are described by stochastic processes with irreversible dynamics. To model these phenomena, we focus on a master equation or a Fokker-Planck equation with rates which violate detailed balance. When the…
We study the classical non-equilibrium statistical mechanics of scalar field theory on the lattice. Steady states are analyzed near and far from equilibrium. The bulk thermal conductivity is computed, including its temperature dependence.…
Different disciplines pursue the aim to develop models which characterize certain phenomena as accurately as possible. Climatology is a prime example, where the temporal evolution of the climate is modeled. In order to compare and improve…
We study the formation of coherent structures in a system with long-range interactions where particles moving on a circle interact through a repulsive cosine potential. Non equilibrium structures are shown to correspond to statistical…
Although coarse-grained models have been widely used to explain exotic phenomena in complex fluids, such as droplet formation in living cells, these conventional approaches often fail to capture the intricate microscopic degrees of freedom…
We consider an aggregation model for two interacting species. The coupling between the species is via their velocities, that incorporate self- and cross-interactions. Our main interest is categorizing the possible steady states of the…
The mathematical physics of mechanical systems in thermal equilibrium is a well studied, and relatively easy, subject, because the Gibbs distribution is in general an adequate guess for the equilibrium state. On the other hand, the…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis,…
We examine energy and particle exchange between finite-sized quantum systems and find a new form of nonequilibrium states. The exchange rate undergoes stepwise evolution in time, and its magnitude and sign dramatically change according to…
Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales. Ecological neutral theory has provided simple predictions…
Non-equilibrium steady states are subject to intense investigations but still poorly understood. For instance, the derivation of Fourier law in Hamiltonian systems is a problem that still poses several obstacles. In order to investigate…
In this paper, we study analytically the statistics of the number of equilibria in pairwise social dilemma evolutionary games with mutation where a game's payoff entries are random variables. Using the replicator-mutator equations, we…
A two-temperature linear spin model is presented that allows an easily understandable introduction to non-equilibrium statistical physics. The model is one that includes the concepts that are typical of more realistic non-equilibrium models…
One of the key features of non-equilibrium steady states (NESS) is the presence of nontrivial probability currents. We propose a general classification of NESS in which these currents play a central distinguishing role. As a corollary, we…
We complete a full classification of non-degenerate traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under (piecewise) smooth perturbations. A striking feature of our analysis is…
An open question in the field of non-equilibrium statistical physics is whether there exists a unique way through which non-equilibrium systems equilibrate irrespective of how far they are away from equilibrium. To answer this question we…
In this paper, we learn dynamics models for parametrized families of dynamical systems with varying properties. The dynamics models are formulated as stochastic processes conditioned on a latent context variable which is inferred from…
For studying the thermodynamic properties of systems using statistical mechanics we propose an ensemble that lies in between the familiar canonical and microcanonical ensembles. From a comparative study of these ensembles we conclude that…
We review some recent developments which make use of the concept of `superstatistics', an effective description for nonequilibrium systems with a varying intensive parameter such as the inverse temperature. We describe how the asymptotic…
We study analytically the dynamics of a generalized p-spin model, starting with a thermalized initial condition. The model presents birth and death of states, hence the dynamics (even starting at equilibrium) may go out of equilibrium when…