[show abstract][hide abstract] ABSTRACT: We discuss relevant aspects of the exact q-thermostatistical treatment for an ideal Fermi system. The grand-canonical exact generalized partition function is given for arbitrary values of the nonextensivity index q, and the ensuing statistics is derived. Special attention is paid to the mean occupation numbers of single-particle levels. Limiting instances of interest are discussed in some detail, namely, the thermodynamic limit, considering in particular both the high- and low-temperature regimes, and the approximate results pertaining to the case q∼1 (the conventional Fermi–Dirac statistics corresponds to q=1). We compare our findings with previous Tsallis’ literature.
Physica A: Statistical Mechanics and its Applications 05/2003; · 1.68 Impact Factor
[show abstract][hide abstract] ABSTRACT: An appropriate redefinition of the Lagrange multipliers entering the q-MaxEnt variational treatment neatly reconciles his formalism with classical thermodynamics. The non-extensive approach is seen to reproduce classical results for all q-values.
Physica A-statistical Mechanics and Its Applications - PHYSICA A. 01/2002; 305(1):41-47.
[show abstract][hide abstract] ABSTRACT: We revisit the celebrated equipartition and virial theorems from a non-extensive viewpoint. We show that both theorems still hold in a non-extensive scenario, independently of the value of Tsallis’ index q.
Physica A: Statistical Mechanics and its Applications. 01/2002;
[show abstract][hide abstract] ABSTRACT: An ideal mixture of parahydrogen (with nuclear spin K=0) and orthohydrogen (with K=1), in statistical weights 1/4 and 3/4, respectively, is used as a test ground for the existence of nonextensivity in chemical physics. We report on a new bound on the nonextensivity parameter q−1 that characterizes generalized thermostatistics à la Tsallis. This bound is obtained on the basis of laboratory measurements of the specific heat of hydrogen. Suggestions are advanced for the performance of improved measurements.
[show abstract][hide abstract] ABSTRACT: Based on the prescription termed the optimal Lagrange multipliers formalism for extremizing the Tsallis entropy indexed by q, it is shown that some key aspects of the treatment of the classical gas problem such as the internal energy and energy correlation are formally identical in both the nonextensive q≠1 and extensive q=1 cases.
[show abstract][hide abstract] ABSTRACT: We show how to reconcile Tsallis’ thermostatistics with thermodynamics’ zeroth law, by recourse to the so-called optimal Lagrange multipliers formalism. The central concept is that of not identifying in the usual fashion the inverse temperature with the Lagrange multiplier associated to the internal energy. Our analysis provides one with compatibility conditions between the additivity of the internal energy and the pseudo-additivity of the generalized entropy. With regards to the first law of thermodynamics, a generalization of Clausius’ equation is advanced.
Physica A: Statistical Mechanics and its Applications. 01/2001;
[show abstract][hide abstract] ABSTRACT: Tsallis’ non-extensive thermostatistics (Tsallis et al., Physica A 261 (1998) 534; Tsallis, in: Abe, Okamoto (Eds.), Nonextensive Statistical Mechanics and its Applications, Lecture Notes in Physics, Springer, Berlin, 2000; Tsallis, Braz. J. Phys. 29 (1991) 1; Plastino and Plastino, in: Ludeña (Ed.), Condensed Matter Theories, Nova Science Publishers, New York, USA, 1996, p. 341; Plastino and Plastino, Braz. J. Phys. 29 (1999) 79) is by now recognized as a new paradigm for statistical mechanical considerations. In a nonextensive scenario, however, the concept of temperature should be handled with some care, as some difficulties ensue (Tsallis, 2000). In this work we discuss this problem and reach some useful conclusions.
Physica A: Statistical Mechanics and its Applications. 01/2001; 295:246-249.
[show abstract][hide abstract] ABSTRACT: We revisit some topics of classical thermostatistics from the perspective of the nonextensive optimal Lagrange multipliers formalism (OLM), a recently introduced technique for dealing with the maximization of Tsallis' information measure. It is shown that equipartition and virial theorems can be reproduced by Tsallis' nonextensive formalism independently of the value of the nonextensivity index.
[show abstract][hide abstract] ABSTRACT: The proper way of averaging is an important question with regards to Tsallis’ Thermostatistics. Three different procedures have been thus far employed in the pertinent literature. The third one, i.e., the Tsallis–Mendes–Plastino (TMP) (Physica A 261 (1998) 534) normalization procedure, exhibits clear advantages with respect to earlier ones. In this work, we advance a distinct (from the TMP-one) way of handling the Lagrange multipliers involved in the extremization process that leads to Tsallis’ statistical operator. It is seen that the new approach considerably simplifies the pertinent analysis without losing the beautiful properties of the Tsallis–Mendes–Plastino formalism.
Physica A: Statistical Mechanics and its Applications. 03/2000;
[show abstract][hide abstract] ABSTRACT: Bacry [Phys. Lett. B 317 (1993) 523] showed that, on the basis of the deformed Poincaré group, special relativity yields a non-additive energy for large systems, i.e., a total energy (of the Universe) which would not be proportional to the number of particles. He consistently argued that this effect could explain (part of) the so-called dark matter. By considering non-interacting spins in the presence of an external magnetic field, it was shown in Portesi et al. [Phys. Rev. E 52 (1995) R3317] that Tsallis’ non-extensive thermostatistics could account for a possible “dark” magnetism (the apparent number of particles being different from the actual one). The work of Pennini et al. [Physica A 258 (1998) 446]; Tsallis et al. [Physica A 261 (1998) 534] uses the so-called “generalized” expectation values, that were for some time considered indispensable in dealing with Tsallis’ formalism. Lately, a different sort of expectation values has been regarded as being superior to the old generalized ones [Pennini et al., Physica A 258 (1998) 446; Tsallis et al., Physica A 261 (1998) 534]. We revisit the dark magnetism question in the light of this new way of computing mean values.
Physica A: Statistical Mechanics and its Applications. 01/2000;
[show abstract][hide abstract] ABSTRACT: The recent proposal by Tsallis of a generalized thermostatistics devised to treat systems endowed with long-range interactions, long-range memory effects, or a fractal-like relevant phase space, has raised interesting and profound issues concerning the properties of general thermostatistical formalisms. In the present paper we identify families of thermostatistical formalisms that share some fundamental characteristics. The canonical ensemble's invariance under uniform translations of the Hamiltonian's energy spectrum is shown to be a universal property verified by any thermostatistical formalism based upon linear mean energy constraints. We also provide multiparametric families of entropies exhibiting Tsallis q-additivity law.
Physica A: Statistical Mechanics and its Applications. 01/1999; 265:590-613.