Tsallis statistics with normalized q-expectation values is thermodynamically stable: illustrations (original) (raw)
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Journal of the Iranian Chemical Society, 2009
In the framework of the Tsallis statistical mechanics, for the spin-1 2 and the harmonic oscillator, we study the change of the population of states when the parameter q is varied; the results show that the difference between predictions of the Boltzmann-Gibbs and Tsallis Statistics can be much smaller than the precision of any existing experiment. Also, the relation between the privilege of rare/frequent event and the value of q is restudied. This relation is shown to be more complicated than the common belief about it. Finally, the convergence criteria of the partition function of some simple model systems, in the framework of Tsallis Statistical Mechanics, is studied; based on this study , we conjecture that q ≤ 1, in the thermodynamic limit.
The Tsallis Formalism of Statistical Mechanics
2008
Considerable interest exists in a general class of alternative statistical distributions proposed by Tsallis [Tsa88] and its effects can be very relevant in the interpretation of thermodynamics and analysed in the framework of non-extensive statistical mechanics. ...
Equivalence of the four versions of Tsallis’s statistics
Journal of Statistical Mechanics: Theory and Experiment, 2005
In spite of its undeniable success, there are still open questions regarding Tsallis's non-extensive statistical formalism, whose founding stone was laid in 1988 in Journal of Statistical Physics. Some of them are concerned with the so-called normalization problem of just how to evaluate expectation values. The Jaynes' MaxEnt approach for deriving statistical mechanics is based on the adoption of (1) a specific entropic functional form S and (2) physically appropriate constraints. The literature on non-extensive thermostatistics has considered, in its historical evolution, four possible choices for the evaluation of expectation values: (i) the 1988 Tsallis original, (ii) the Curado-Tsallis version, (iii) the Tsallis-Mendes-Plastino version, and (iv) the Tsallis-Mendes-Plastino version, but using centred operators as constraints. The 1988 version was promptly abandoned and replaced, mostly with versions (ii) and (iii). We will here (a) show that the 1988 version is as good as any of the others, (b) demonstrate that the four cases can be easily derived from just one (any) of them, i.e., the probability distribution function in each of these four instances may be evaluated with a unique formula, and (c) numerically analyse some consequences that emerge from these four choices.
Generalized Entropies and Statistical Mechanics
2004
We consider the problem of defining free energy and other thermodynamic functions when the entropy is given as a general function of the probablity distribution, including that for non extensive forms. We find that the free energy, which is central to the determination of all other quantities, can be obtained uniquely numerically ebven when it is the root of a transcendental equation. In particular we study the cases for Tsallis form and a new form proposed by us recently. We compare the free energy, the internal energy and the specific heat of a simple system two energy states for each of these forms.
Is Tsallis Thermodynamics Nonextensive
Physical Review Letters, 2002
Within the Tsallis thermodynamics framework, and using scaling properties of the entropy, we derive a generalization of the Gibbs-Duhem equation. The analysis suggests a transformation of variables that allows standard thermodynamics to be recovered. Moreover, we also generalize Einstein's formula for the probability of a fluctuation to occur by means of the maximum statistical entropy method. The use of the proposed transformation of variables also shows that fluctuations within Tsallis statistics can be mapped to those of standard statistical mechanics.
Tsallis thermostatics as a statistical physics of random chains
Physical Review E, 2017
In this paper we point out that the generalized statistics of Tsallis-Havrda-Charvát can be conveniently used as a conceptual framework for statistical treatment of random chains. In particular, we use the path-integral approach to show that the ensuing partition function can be identified with the partition function of a fluctuating oriented random loop of arbitrary length and shape in a background scalar potential. To put some meat on the bare bones, we illustrate this with two statistical systems; Schultz-Zimm polymer and relativistic particle. Further salient issues such as the P SL(2, R) transformation properties of Tsallis' inverse-temperature parameter and a grandcanonical ensemble of fluctuating random loops related to the Tsallis-Havrda-Charvát statistics are also briefly discussed.
Irreversible processes: The generalized affinities within Tsallis statistics
Physica A: Statistical Mechanics and its Applications, 1998
Within the generalized statistical mechanics introduced recently by Tsallis, the generalized form of the a nities (the quantities which drive a process in the theory of irreversible thermodynamics) was derived. The a nities were obtained by considering changes in the generalized entropy S AUB q of a system composed by two subsystems A and B. The non-extensive character of the Tsallis entropy is taken into account. At the end, the equilibrium condition is discussed and the zeroth law in the framework of the generalized thermodynamics is consistently recovered: as in the usual case, two systems which are in equilibrium with a third one are necessarily in equilibrium among them and share the same temperature.