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The variance of the number of particles in a set is an important quantity in understanding the statistics of non-interacting fermionic systems in low dimensions. An exact map of their ground state in a harmonic trap in one and two…
An explicit formula for the interaction energy of $n$ vortices in the abelian Higgs (or Ginzburg-Landau) model is derived, valid in the regime where all vortices are close to one another. An immediate consequence of this formula is that the…
Recently Abe (arXiv:cond-mat/1005.5110v1) claimed that the q-entropy of nonextensive statistical mechanics cannot be generalized for the continuous variables and therefore can be used only in the discrete case. In this letter, we show that…
The question of deriving general force/flux relationships that apply out of the linear response regime is a central topic of theories for nonequilibrium statistical mechanics. This work applies an information theory perspective to compute…
In nonextensive statistical mechanics, two kinds of definitions have been considered for expectation valu of a physical quantity: one is the ordinary definition and the other is the normalized q-expectation value employing the escort…
We propose a generalisation of Gibbs' statistical mechanics into the domain of non-negligible phase space correlations. Derived are the probability distribution and entropy as a generalised ensemble average, replacing…
The no-pumping theorem states that seemingly natural driving cycles of stochastic machines fail to generate directed motion. Initially derived for single particle systems, the no-pumping theorem was recently extended to many-particle…
We discuss the dynamics and thermodynamics of systems with weak long-range interactions. Generically, these systems experience a violent collisionless relaxation in the Vlasov regime leading to a (usually) non-Boltzmannian quasi stationary…
The incomplete nonextensive statistics in the canonical and microcanonical ensembles is explored in the general case and in a particular case for the ideal gas. By exact analytical results for the ideal gas it is shown that taking the…
We show that fractional exclusion statistics is manifested in general in interacting systems and we discuss the conjecture recently introduced (J. Phys. A: Math. Theor. 40, F1013, 2007), according to which if in a thermodynamic system the…
Quite unexpectedly, kinetic theory is found to specify the correct definition of average value to be employed in nonextensive statistical mechanics. It is shown that the normal average is consistent with the generalized Stosszahlansatz…
Self-gravitating systems are generally thought to behavior non-extensively due to the long-range nature of gravitational forces. We obtain a relation between the nonextensive parameter q of Tsallis statistics, the temperature gradient and…
A statistical treatment of finite unbound systems in the presence of collective motions is presented and applied to a classical Lennard-Jones Hamiltonian, numerically simulated through molecular dynamics. In the ideal gas limit, the flow…
We study and characterize a new dynamical regime of underdamped particles in a tilted washboard potential. We find that for small friction in a finite range of forces the particles move essentially nondispersively, that is, coherently, over…
We propose a novel approach in the study of transport phenomena in dense systems or systems with long range interactions where multiple particle interactions must be taken into consideration. Within Boltzmann's kinetic formalism, we study…
We construct classes of stochastic differential equations with fluctuating friction forces that generate a dynamics correctly described by Tsallis statistics and nonextensive statistical mechanics. These systems generalize the way in which…
We study the thermodynamic properties of solid and metal electrons in the nonextensive quantum statistics with a nonextensive parameter transformation. First we study the nonextensive grand canonical distribution function and the…
Classical, self-consistent theory of statistical mechanics was developed for the thermodynamic and conservative Hamiltonian systems. Later there were many attempts (Sinai-Bowen-Ruelle's temperature, Tsallis' non-extensive theory) to apply…
A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating…
It has been observed empirically that two dimensional vortices tend to cluster forming a giant vortex. To account for this observation Onsager introduced a concept of negative absolute temperature in equilibrium statistical mechanics. In…