Related papers: Statistical theory of self-similarly distributed f…
We show how statistical thermodynamics can be formulated in situations in which thermodynamics applies, while equilibrium statistical mechanics does not. A typical case is, in the words of Landau and Lifshitz, that of partial (or…
The asymptotic correspondence between the probability mass function of the $q$-deformed multinomial distribution and the $q$-generalised Kullback-Leibler divergence, also known as Tsallis relative entropy, is established. The probability…
This paper applies the formalism of classical, Gibbs-Boltzmann statistical mechanics to the phenomenon of non-thermal damage. As an example, a non-thermal fiber-bundle model with the global uniform (meanfield) load sharing is considered.…
A new formulation of statistical mechanics is put forward according to which a random variable characterizing a macroscopic body is postulated to be infinitely divisible. It leads to a parametric representation of partition function of an…
A Cahn-Hilliard-type theory for hydrodynamic fluctuations is proposed that gives a quantitative description of the slowly evolving spatial correlations and structures in density and flow fields in the early stages of evolution of freely…
We study scaling properties of stochastic aggregation processes in one dimension. Numerical simulations for both diffusive and ballistic transport show that the mass distribution is characterized by two independent nontrivial exponents…
The statistical equilibrium properties of the linear sigma model are studied, with a view towards characterizing the field configurations employed as initial conditions for numerical simulations of the formation of disoriented chiral…
By using the maximum entropy principle with Tsallis entropy we obtain a fragment size distribution function which undergoes a transition to scaling. This distribution function reduces to those obtained by other authors using Shannon…
Generalized numbers, arithmetic operators and derivative operators, grouped in four classes based on symmetry features, are introduced. Their building element is the pair of $q$-logarithm/$q$-exponential inverse functions. Some of the…
Random matrix models provide a phenomenological description of a vast variety of physical phenomena. Prominent examples include the eigenvalue statistics of quantum (chaotic) systems, which are conveniently characterized using the spectral…
We reveal the critical properties of the phase transition towards superfluid order that has been proposed to occur in large spin fermionic systems. For this purpose, we consider the bosonic field theory for fluctuations of the complex…
Multiplicative cascades have been used in turbulence to generate fields with multifractal statistics and long-range correlations. Examples of continuous and causal stochastic processes which generate such a random field have been carefully…
A general statistical thermodynamic theory that considers given sequences of x-integers to play the role of particles of known type in an isolated elastic system is proposed. By also considering some explicit discrete probability…
Relativistic particle production often requires the use of Tsallis statistics to account for the apparently power-like behavior of transverse momenta observed in the data even at a few GeV/c. In such an approach this behavior is attributed…
Time evolution equations for dynamical systems can often be derived from generating functionals. Examples are Newton's equations of motion in classical dynamics which can be generated within the Lagrange or the Hamiltonian formalism. We…
A quantum field theory is described which is a supersymmetric classical model. -- Supersymmetry generators of the system are used to split its Liouville operator into two contributions, with positive and negative spectrum, respectively. The…
As the quantification of metabolism, nonequilibrium steady states play a central role in living matter, but are beyond the purview of equilibrium statistical mechanics. Here we develop a fermionic theory of nonequilibrium steady states in…
An approach to the description of subdynamics inside non-relativistic quantum field theory is presented, in which the notions of relevant observable, time scale and complete positivity of the time evolution are stressed. A scattering theory…
It is argued that the factorization of compound probability over subsystems is a consequence of the existence of thermodynamic equilibrium in the composite system having Tsallis entropy. So it should be respected by all exact calculations…
Fractional occupation numbers can be used in density functional theory to create a symmetric Kohn-Sham potential, resulting in orbitals with degenerate eigenvalues. We develop the corresponding perturbation theory and apply it to a system…