Related papers: Canonical and non-canonical equilibrium distributi…
When a physical system is driven away from equilibrium, the statistical distribution of its dynamical trajectories informs many of its physical properties. Characterizing the nature of the distribution of dynamical observables, such as a…
For classical discrete system under constant composition, we theoretically examine origin of nonlinearity in thermodynamic (so-called canonical) average w.r.t. many-body interactions, in terms of geometrical information in configuratin…
The two-body potential of systems with long-range interactions decays at large distances as $V(r)\sim 1/r^\alpha$, with $\alpha\leq d$, where $d$ is the space dimension. Examples are: gravitational systems, two-dimensional hydrodynamics,…
Reaction-diffusion systems driven far from thermodynamic equilibrium through the injection of energy can support multiple distinct spatial patterns that persist as long-lived dynamical phases. The stability of these metastable phases is not…
Involvement of the environment is indispensable for establishing the statistical distribution of system. We analyze the statistical distribution of a quantum system coupled strongly with a heat bath. This distribution is determined by…
The physical meaning of entropy is analyzed in the context of statistical, nuclear, atomic physics and cosmology. Only the microcanonical Boltzmann entropy leads to no contradictions in several simple, elementary and for thermodynamics…
We discuss a relativistic diffusion in the proper time in an approach of Schay and Dudley. We derive (Langevin) stochastic differential equations in various coordinates.We show that in some coordinates the stochastic differential equations…
The classical theory of linear response applies to statistical mechanics close to equilibrium. Away from equilibrium, one may describe the microscopic time evolution by a general differentiable dynamical system, identify nonequilibrium…
We study generalizations of It\^{o}-Langevin dynamics consistent within nonextensive thermostatistics. The corresponding stochastic differential equations are shown to be connected with a wide class of nonlinear Fokker-Planck equations…
The population dynamics and stability of ecosystems of interacting species is studied from the perspective of non-equilibrium thermodynamics by assuming that species, through their biotic and abiotic interactions, are units of entropy…
Systems out of equilibrium, in stationary as well as in nonstationary regimes, display a linear response to energy impulses simply expressed as the sum of two specific temporal correlation functions. There is a natural interpretation of…
Statistical physics aims to describe properties of macroscale systems in terms of distributions of their microscale agents. Its central tool is the maximization of entropy, a variational principle. We review the history of this principle,…
Traditional derivation of Gibbs canonical distribution and the justification of thermodynamics are based on the assumption concerning an isoenergetic ergodicity of a system of $n$ weakly interacting identical subsystems and passage to the…
Within the frames of the analytical mechanics the method of the description of dynamics of nonequilibrium systems of potentially interacting elements is develops. The method is based on an opportunity of representation of nonequilibrium…
The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and…
We consider three equilibrium concepts proposed in the literature for time-inconsistent stopping problems, including mild equilibria, weak equilibria and strong equilibria. The discount function is assumed to be log sub-additive and the…
We study a process of anomalous diffusion, based on intermittent velocity fluctuations, and we show that its scaling depends on whether we observe the motion of many independent trajectories or that of a Liouville-like equation driven…
We formulate a model that describes the escape dynamics in a leaky chaotic system in which the size of the leak depends on the number of the in-falling particles. The basic motivation of this work is the astrophysical process which…
Stationary non-equilibrium states describe steady flows through macroscopic systems. Although they represent the simplest generalization of equilibrium states, they exhibit a variety of new phenomena. Within a statistical mechanics…
Motivated by stochastic convection-diffusion problems we derive a posteriori error estimates for non-stationary non-linear convection-diffusion equations acting as a deterministic paradigm. The problem considered here neither fits into the…