Related papers: Statistical Mechanics: A Selective Review of Two C…
The microscopic model in which nodes interacting with each other are statistical systems is introduced. The nodes conditions are connected with a string of distinct microscopic configurations and depend on external parameters (pressure and…
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…
We study the sum of first passage times along an arbitrary cycle made up of N>2 states of a small physical system. We show that, if the system is at thermodynamic equilibrium, this sum follows the same probability distribution regardless of…
Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem. The quantum state of a microscopic system is defined to correspond to…
Quantum statistics originate from the physics of state preparation. It is therefore wrong to think of quantum states as fundamental. In fact, quantum states are merely summaries of dynamical processes that randomize the properties of the…
Equilibrium statistical mechanics rests on the assumption of ergodic dynamics of a system modulo the conservation laws of local observables: extremization of entropy immediately gives Gibbs' ensemble (GE) for energy conserving systems and a…
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,…
How stochastic, microscopic events generate deterministic, macroscopic properties is a fundamental question in physics. We address this question by developing a quantum master equation model for concentrated radical solutions, where random…
The present paper is meant to give a simple introduction to the problem of the connection between microscopic dynamics and statistical laws. For sake of simplicity, we mostly refer to non-dissipative dynamics, since dissipation adds…
Physics explains the laws of motion that govern the time evolution of observable properties and the dynamical response of systems to various interactions. However, quantum theory separates the observable part of physics from the…
Statistical mechanics descriptions of the second law of thermodynamics generally imply point-like particles driven by a dissipative overall mechanism for their simultaneous time-evolution. As the number of involved particles grows larger,…
Consider a statistical model with an epistemic restriction such that, unlike in classical mechanics, the allowed distribution of positions is fundamentally restricted by the form of an underlying momentum field. Assume an agent (observer)…
Many complex systems are representable as macroscopic set of elements which interact by simple rules. The complex macroscopically relevant phenomena are then the result of the generic emergence of a space-time multi-scale dynamics. Critical…
We are pleased to present a Special Section on Statistics and Astronomy in this issue of the The Annals of Applied Statistics. Astronomy is an observational rather than experimental science; as a result, astronomical data sets both small…
Statistical systems are conceived from the standpoint of statistical mechanics, as made of a (generally large) number of identical units and exhibiting a (generally large) number of different configurations (microstates), among which only…
Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new…
In this paper I propose a new way for counting the microstates of a system out of equilibrium. As, according to quantum mechanics, things happen as if a given particle can be found in more than one state at once, I extend this concept to…
The theoretical study of the self-organization of two-dimensional and geophysical turbulent flows is addressed based on statistical mechanics methods. This review is a self-contained presentation of classical and recent works on this…
It is shown that due to memory effects the complex behaviour of components in a stochastic system can be transmitted to macroscopic evolution of the system as a whole. Within the Markov approximation widely using in ordinary statistical…
We give an introduction to phase transitions in the steady states of systems that evolve stochastically with equilibrium and nonequilibrium dynamics, the latter defined as those that do not possess a time-reversal symmetry. We try as much…