Related papers: Multicanonical distribution: Statistical equilibri…
Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to…
The foundations of the Boltzmann-Gibbs (BG) distributions for describing equilibrium statistical mechanics of systems are examined. Broadly, they fall into: (i) probabilistic paaroaches based on the principle of equal a priori probability…
Nonequilibrium complex systems are often effectively described by the mixture of different dynamics on different time scales. Superstatistics, which is "statistics of statistics" with two largely separated time scales, offers a consistent…
Recent investigations of turbulent circulation fluctuations have uncovered substantial insights into the statistical organization of flow structures and revealed unexpected geometric features of turbulent intermittency. Of particular…
We show insurmountable contradictions which arise if statistical ensembles are considered a consequence of the influence of the environment of the physical systems. We regard the multiplicity of states with a definite energy value as a…
A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems…
We extend the canonical Gibbs distribution, originally formulated for systems at equilibrium, to systems driven out of equilibrium. The stochastic dynamics of a small system are described by a probability distribution over discrete energy…
There are three levels of description in classical statistical mechanics, the microscopic/dynamic, the macroscopic/statistical and the thermodynamic. At one end there is a well-used concept of equilibrium in thermodynamics and at the other…
Starting from microcanonical basis with the principle of equal a priori probability, it is found that, besides ordinary Boltzmann-Gibbs theory with the exponential distribution, a theory describing systems with power-law distributions can…
The paper is devoted to the construction of the superstatistical description for nonequilibrium Markovian systems. It is based on Kirchhoff's diagram technique and the assumption on the system under consideration to possess a wide variety…
Equilibrium statistical mechanics is intended to link the microscopic dynamics of particles to the thermodynamic laws for macroscopic quantities. However, the modern statistical theory is faced with significant difficulties, as applied to…
Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important role in analysis of hierarchical complex dynamical systems. Yet, its "canonical" formulation in terms of a single nuisance parameter…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
Multiscale thermodynamics is a theory of relations among levels of investigation of complex systems. It includes the classical equilibrium thermodynamics as a special case but it is applicable to both static and time evolving processes in…
A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary…
The theory of superstatistics, originally proposed for the study of complex nonequilibrium systems, has recently been extended to studies of small systems interacting with a finite environment, because such systems display interestingly…
A heuristic generalization of the Boltzmann-Gibbs microcanonical entropy is proposed, able to describe meta-equilibrium features and evolution of macroscopic systems. Despite its simple-minded derivation, such a function of "collective…
Depending on the exact experimental conditions, the thermodynamic properties of physical systems can be related to one or more thermostatistical ensembles. Here, we survey the notion of thermodynamic temperature in different statistical…
The theory of small-system thermodynamics was originally developed to extend the laws of thermodynamics to length scales of nanometers. Here we review this "nanothermodynamics," and stress how it also applies to large systems that subdivide…
The aim of this paper is to introduce a new technique for calculation of observables, in particular multiplicity distributions, in various statistical ensembles at finite volume. The method is based on Fourier analysis of the grand…