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The understanding of the emergence of equilibrium statistical mechanics has progressed significantly thanks to developments from typicality, canonical and dynamical, and from the eigenstate thermalization hypothesis. Here we focus on a…
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…
Ability of dynamical systems to relax to equilibrium has been investigated since the invention of statistical mechanics, which establishes the connection between dynamics of many-body Hamiltonian systems and phenomenological thermodynamics.…
We study fluctuations of pressure in equilibrium for classical particle systems. In equilibrium statistical mechanics, pressure for a microscopic state is defined by the derivative of a thermodynamic function or, more mechanically, through…
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 review the general aspects of the concept of temperature in equilibrium and non-equilibrium statistical mechanics. Although temperature is an old and well-established notion, it still presents controversial facets. After a short…
The modelling of traffic flow using methods and models from physics has a long history. In recent years especially cellular automata models have allowed for large-scale simulations of large traffic networks faster than real time. On the…
Pattern-forming nonequilibrium systems are ubiquitous in nature, from driven quantum matter and biological life forms to atmospheric and interstellar gases. Identifying universal aspects of their far-from-equilibrium dynamics and statistics…
This article traces the development of fluctuation theory and its deep connection to irreversibility, from equilibrium to near-equilibrium, and finally to far-from-equilibrium systems. Classical fluctuation theorems, which capture the…
On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated…
Many biological, chemical, and physical systems are underpinned by stochastic transitions between equilibrium states in a potential energy. Here, we consider such transitions in a minimal model with two possible competing pathways, both…
We analyze F\"urth's 1933 classical uncertainty relations in the modern language of stochastic differential equations. Our interest is motivated by applications to non-equilibrium classical statistical mechanics. We show that F\"urth's…
Using the system-bath model Hamiltonian this thesis covers the equilibrium and out of equilibrium properties of quantum open systems. Topics included are the calculation of thermodynamical quantities of open systems, derivation of quantum…
The article is dedicated to discussion of irreversibility and foundation of statistical mechanics "from the first principles". Taking into account infinitesimal and, as it seems, neglectful for classical mechanics fluctuations of the…
We present the stochastic thermodynamics analysis of an open quantum system weakly coupled to multiple reservoirs and driven by a rapidly oscillating external field. The analysis is built on a modified stochastic master equation in the…
In statistical mechanics, measuring the number of available states and their probabilities, and thus the system's entropy, enables the prediction of the macroscopic properties of a physical system at equilibrium. This predictive capacity…
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics like work, heat and entropy production to the level of individual trajectories of well-defined…
Employing the stochastic wave function method, we study quantum features of stochastic entropy production in nonequilibrium processes of open systems. It is demonstarted that continuous measurements on the environment introduce an…
We briefly review the present status of nonextensive statistical mechanics. We focus on (i) the central equations of the formalism, (ii) the most recent applications in physics and other sciences, (iii) the {\it a priori} determination…
Biological machines like molecular motors and enzymes operate in dynamic cycles representable as stochastic flows on networks. Current stochastic dynamics describes such flows on fixed networks. Here, we develop a scalable approach to…