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We study ergodic properties of stochastic dissipative systems with additive noise. We show that the system is uniformly exponentially ergodic provided the growth of nonlinearity at infinity is faster than linear. The abstract result is…

We study almost sure limiting behavior of extreme and intermediate order statistics arising from strictly stationary sequences. First, we provide sufficient dependence conditions under which these order statistics converges almost surely to…

We develop the stochastic approach to thermodynamics based on the stochastic dynamics, which can be discrete (master equation) continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of…

We prove regularity and stochastic homogenization results for certain degenerate elliptic equations in nondivergence form. The equation is required to be strictly elliptic, but the ellipticity may oscillate on the microscopic scale and is…

The study of microscopic protein dynamics has historically presented significant challenges to researchers seeking to develop a comprehensive and detailed description of its diverse and intriguing features. Recent experimental and…

How do networks of relationships evolve over time? We analyse a dataset tracking the social interactions of 900 individuals over four years. Despite continuous shifts in individual relationships, the macroscopic structural properties of the…

For a class of processes modeling the evolution of a spatially structured population with migration and a logistic local regulation of the reproduction dynamics, we show convergence to an upper invariant measure from a suitable class of…

Diffusion with stochastic resetting is a paradigm of resetting processes. Standard renewal or master equation approach are typically used to study steady state and other transport properties such as average, mean squared displacement etc.…

We start by reviewing recent probabilistic results on ergodic sums in a large class of (non-uniformly) hyperbolic dynamical systems. Namely, we describe the central limit theorem, the almost-sure convergence to the gaussian and other stable…

To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime of a system. The statistical distributions which can be obtained out of the mesoscopic description characterizing the behaviour of a…

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…

Dynamics near and far away from thermal equilibrium is studied within the framework of Langevin equations. A stochasticity-dissipation relation is proposed to emphasize the equal importance of the stochastic and deterministic forces in…

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 consider stationary stochastic dynamical systems evolving on a compact metric space, by perturbing a deterministic dynamics with a random noise, added according to an arbitrary probabilistic distribution. We prove the maximal and…

In this note we present two types of biological models which have interesting ergodic and chaotic properties. The first type are one-dimensional transformations, like a logistic map, which are used to describe the change in population size…

The conceptual difference between equilibrium and non-equilibrium steady state (NESS) is well established in physics and chemistry. This distinction, however, is not widely appreciated in dynamical descriptions of biological populations in…

The selection of an equilibrium state by maximising the entropy of a system, subject to certain constraints, is often powerfully motivated as an exercise in logical inference, a procedure where conclusions are reached on the basis of…

The vast majority of the literature on learning dynamical systems or stochastic processes from time series has focused on stable or ergodic systems, for both Bayesian and frequentist inference procedures. However, most real-world systems…

Stochastic thermodynamics provides a useful set of tools to analyze and constrain the behavior of far from equilibrium systems. In this paper, we report an application of ideas from stochastic thermodynamics to the problem of membrane…

Understanding the stochastic properties of conductance fluctuations in disordered mesoscopic systems is fundamental to quantum transport. In this work, we investigate the multifractal and ergodic properties of the fictitious time series of…