Nonextensive thermodynamic functions in the Schrödinger-Gibbs ensemble

Nonextensive thermodynamic functions in the Schrödinger-Gibbs ensemble.

Schrödinger suggested that thermodynamical functions cannot be based on the gratuitous allegation that quantum-mechanical levels (typically the orthogonal eigenstates of the Hamiltonian operator) are the only allowed states for a quantum system [E. Schrödinger, Statistical Thermodynamics (Courier Dover, Mineola, 1967)]. Different authors have interpreted this statement by introducing density di...

Probabilistic properties of nonextensive thermodynamic

Based on the Tsallis entropy, the nonextensive thermodynamic properties are studied as a qdeformation of classical statistical results using only probabilistic methods and straightforward calculations. It is shown that the constant in the Tsallis entropy depends on the deformation parameter and must be redefined to recover the usual thermodynamic relations. The notions of variance and covarianc...

Quasicanonical Gibbs distribution and Tsallis nonextensive statistics

We derive and study quasicanonical Gibbs distribution function which is characterized by the thermostat with finite number of particles (quasithermostat). We show that this naturally leads to Tsallis nonextensive statistics and thermodynamics, with Tsallis parameter q is found to be related to the number of particles in the quasither-mostat. We show that the chi-square distribution of fluctuati...

Gibbs Ensemble Techniques

The Gibbs ensemble of a vortex filament

Certain investigations of turbulent 3-D fluids seem to indicate that the vorticity field of the fluid is strongly concentrated along thin structures, called vortex filaments. A. Chorin has developed a statistical-mechanics theory of vortex filaments to describe the statistics of turbulent flows, see [4]. In his investigations vortex filaments are modelled by trajectories of self-avoiding walks ...