arXiv subjects

Roberto Luzzi

Publications and source records attributed to Roberto Luzzi.

21 records · Page 2Linked to original sources

arXiv2004

Entropy: Mystery and Controversy. Plethora of Informational-Entropies and Unconventional Statistics

Some general considerations on the notion of entropy in physics are presented. An attempt is made to clarify the question of the differentiation between physical entropy (the Clausius-Boltzmann one) and quantities called entropies associated to Information Theory, which are in fact generating functionals for the derivation of probability distributions and not thermodynamic functions of state. The role of them in the construction of the so-called Unconventional Statistical Mechanics, and the meaning and use of the latter, is discussed. Particular attention is given to the situation involving far-from-equilibrium systems.

cond-mat.stat-mech↗

arXiv2004

Competing Styles of Statistical Mechanics: I. Systematization and Clarification in a General Theory

Competing styles of Statistical Mechanics have been introduced as practical succedaneous to the conventional well established Boltzmann-Gibbs statistical mechanics, when in the use of the latter the researcher is impaired in his/her capacity for satisfying the Criteria of Efficiency and/or Sufficiency in statistics [Fisher, 1922], that is, a failure in the characterization (presence of fractality, scaling, etc.) of the system related to some aspect relevant to the given physical situation. To patch this limitation on the part of the observer, in order to make predictions on the values of observables and response functions, are introduced unconventional approaches. We present a detailed description of their construction and a clarification of its scope and interpretation. Also, resorting to the use of the particular case of Renyi's unconventional statistics is built a nonequilibrium ensemble formalism. The unconventional distribution functions of fermions and bosons are obtained, and in a follow-up article [cond-mat/0306247] we describe applications to the study of experimental results in semiconductor physics and in electro-chemistry involving nanometric scales and fractal-like structures, and some additional theoretical analysis is added. PACS: 05.70.Ln, 82.20.Mj, 82.20.Db Keywords: Nonequilibrium Ensemble Formalism; Generalized Informational Entropies; Generalized Statistics; Nonextensive Statistics; Renyi Statistics; Escort Probability.

cond-mat.stat-mech↗

arXiv2004

Competing Styles of Statistical Mechanics: II. Comparison of Theory and Experiment and Further Illustrations

In the present follow-up article of a previous one [1] we illustrate the use of the Unconventional Statistical Mechanics described and discussed in the latter. This is done via the analysis, resorting to Renyi approach, of experimental results in the case of so-called "anomalous" luminescence in nanometric quantum wells in semiconductor heterostructures, and the so-called "anomalous" cyclic voltammetry in fractal-like electrodes in microbatteries. Also a purely theoretical analysis is done in the cases of an ideal gas and of radiation comparing the conventional and unconventional approaches. In all of these situations it is discussed which is the failure to satisfy the Criteria of Efficiency and/or Sufficiency thus requiring to resort to the unconventional approach, and what determines the value of the infoentropic index in each case, and its dependence on the system characteristics. Moreover, on the basis of the results we obtain, it is conjectured that the infoentropic index may satisfy what we call a law defining a "path to sufficiency". PACS: 05.70.Ln; 82.20.Mj; 82.20.Db Keywords: Renyi Statistics; Escort Probability; Fractal Structured Systems; Power Law Properties.

cond-mat.stat-mech↗