Related papers: Statistical mechanics of damage phenomena
The present paper studies a large class of temperature dependent probability distributions and shows that entropy and energy can be defined in such a way that these probability distributions are the equilibrium states of a generalized…
The most complicated phenomena of equilibrium statistics, phase separations and transitions of various order and critical phenomena, can clearly and sharply be seen even for small systems in the topology of the curvature of the…
We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state…
The mean-field thermodynamic limit is studied for a class of isolated Newtonian N-body systems whose Hamiltonian admits several invariants of motion. It is shown that the macrostates of individual members of a statistical equilibrium…
The kinetic energy distribution function satisfying the Boltzmann equation is studied analytically and numerically for a system of inelastic hard spheres in the case of binary collisions. Analytically, this function is shown to have a…
Boltzmann's principle S(E,N,V)=k\ln W relates the entropy to the geometric area e^{S(E,N,V)} of the manifold of constant energy in the N-body phase space. From the principle all thermodynamics and especially all phenomena of phase…
An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is…
We numerically study a one-dimensional system of $N$ classical localized planar rotators coupled through interactions which decay with distance as $1/r^\alpha$ ($\alpha \ge 0$). The approach is a first principle one (\textit{i.e.}, based on…
The basic aspects of both Boltzmann-Gibbs (BG) and nonextensive statistical mechanics can be seen through three different stages. First, the proposal of an entropic functional ($S_{BG} =-k\sum_i p_i \ln p_i$ for the BG formalism) with the…
We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at…
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 briefly review Boltzmann-Gibbs and nonextensive statistical mechanics as well as their connections with Fokker-Planck equations and with existing central limit theorems. We then provide some hints that might pave the road to the proof of…
We consider the problem of constructing a thermodynamic theory of non-equilibrium steady states as a formal extension of the equilibrium theory. Specifically, studying a particular system, we attempt to construct a phenomenological theory…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
Statistical mechanics describes interaction between particles of a physical system. Particle properties of the system can be modelled with a random field on a lattice and studied at different distance scales using renormalization group…
A statistical thermodynamic approach of moving particles forming an elastic body is presented which leads to reveal molecular-mechanical properties of classical and nonextensive dynamical systems. We derive the Boltzmann-Gibbs (BG) entropy…
The scalar field theory and the scalar electrodynamics quantized in the flat gap are considered. The dynamical effects arising due to the boundary presence with two types of boundary conditions (BC) satisfied by scalar fields are studied.…
A geometric approach to the friction phenomena is presented. It is based on the holographic view which has recently been popular in the theoretical physics community. We see the system in one-dimension-higher space. The heat-producing…
People are well aware that, inherently, certain small-scale nonchaotic particle movements are not governed by thermodynamics. Usually, such phenomena are studied by kinetic theory and their energy properties are considered "trivial". In…
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…