Related papers: Canonical Thermodynamics
We derive the continuous canonical distribution only by requiring the extensivity of the mean energy and the multiplicative probabilistic composition rule. The derivation is independent of the thermodynamic limit and moreover it does not…
A thermodynamic system of non-interacting quantum particles changes its statistical distribution formulas if there is a universal limitation for the size of energetic quantum leaps (magnitude of quantum leaps smaller than Planck energy). By…
For a closed bi-partite quantum system partitioned into system proper and environment we interprete the microcanonical and the canonical condition as constraints for the interaction between those two subsystems. In both cases the possible…
The paper discusses the physical groundlessness of the models used for the derivation of canonical distribution and provides the experimental data demonstrating the incompleteness of quantum mechanics. The possibility of using statistical…
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…
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…
We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in…
Several approximations are made to study the microcanonical formalism that are valid in the thermodynamics limit. Usually it is assumed that: 1)Stirling approximation can be used to evaluate the number of microstates; 2) the surface entropy…
The retainability of canonical distributions for a Brownian particle controlled by a time-dependent harmonic potential is investigated in the overdamped and underdamped situations, respectively. Because of different time scales, the…
We propose a definition of microcanonical and canonical statistical ensembles based on the concept of density of states. This definition applies both to the classical and the quantum case. For the microcanonical case this allows for a…
The issue of the thermodynamics of a system of distinguishable particles is discussed in this paper. In constructing the statistical mechanics of distinguishable particles from the definition of Boltzmann entropy, it is found that the…
In the field of classical discrete systems, specifically substitutional alloys, this study introduces a stochastic thermodynamic approach to address nonlinearity within a canonical ensemble. This approach establishes a nonlinear…
The grand canonical ensemble lies at the core of quantum and classical statistical mechanics. A small system thermalizes to this ensemble while exchanging heat and particles with a bath. A quantum system may exchange quantities represented…
Traditional derivation of Gibbs canonical distribution and the justification of thermodynamics are based on the assumption concerning an isoenergetic ergodicity of a system of $n$ weakly interacting identical subsystems and passage to the…
The microcanonical ensemble is in important physical situations different from the canonical one even in the thermodynamic limit. In contrast to the canonical ensemble it does not suppress spatially inhomogeneous configurations like phase…
We consider a stochastic $N$-particle system on a torus in which each particle moving freely can instantaneously thermalize according to the particle configuration at that instant. Following [2], we show that the propagation of chaos does…
The analytical probability distribution of finite systems obeying Bose-Einstein statistics in one, two, and three dimensions are investigated by using a canonical ensemble approach. Starting from the canonical partition function of the…
The basic idea of a microscopic understanding of Thermodynamics is to derive its main features from a microscopic probability distribution. In such a vein, we investigate the thermal statistics of quasi-probabilities's semi-classical…
The problem of factorization of a nonextensive probability distribution is discussed. It is shown that, in general, the correlation energy between the correlated subsystems in the canonical composite system can not be neglected even in the…
For studying the thermodynamic properties of systems using statistical mechanics we propose an ensemble that lies in between the familiar canonical and microcanonical ensembles. From a comparative study of these ensembles we conclude that…