NONEXTENSIVE STATISTICAL MECHANICS APPROACH TO THE SOMMERFELD MODEL FOR METALLIC ELEMENTS

2013 ◽  
Vol 27 (31) ◽  
pp. 1350181 ◽  
Author(s):  
KAMEL OURABAH ◽  
MOULOUD TRIBECHE
Keyword(s):  
Heat Capacity ◽  
Statistical Mechanics ◽  
Reasonable Agreement ◽  
Chemical Potential ◽  
Metallic Elements ◽  
Nonextensive Statistical Mechanics ◽  
Usual Model ◽  
Dirac Distribution ◽  
Entropic Index ◽  
Theory And Experiment

Using the generalized Fermi–Dirac distribution function arising from Tsallis statistical mechanics, we revisit the Sommerfeld model for metallic elements. The chemical potential, the total energy and the heat capacity are calculated. It is shown that the linearity between the heat capacity and the temperature is q-dependent, where q stands for the entropic index. In the limit q→1, the results of the usual model are recovered. Comparisons are made with experimental data and with the values of the usual model. The Pauli magnetic susceptibility is found not affected by the electron nonextensivity. Our results suggest that we can rely on the generalized nonextensive Sommerfeld model to expect achievement of reasonable agreement between theory and experiment. They may aid to constrain the values of the nonextensive parameter q for metallic elements and to determine more clearly the reality of nonextensive effects.

scholarly journals Chiral Phase Transition in Linear Sigma Model with Nonextensive Statistical Mechanics

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Ke-Ming Shen ◽  
Hui Zhang ◽  
De-Fu Hou ◽  
Ben-Wei Zhang ◽  
En-Ke Wang
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Statistical Mechanics ◽  
Sigma Model ◽  
Chemical Potential ◽  
Linear Sigma Model ◽  
Nonextensive Statistical Mechanics ◽  
Chiral Phase ◽  
Chiral Phase Transition ◽  
Lower Temperature

From the nonextensive statistical mechanics, we investigate the chiral phase transition at finite temperature T and baryon chemical potential μB in the framework of the linear sigma model. The corresponding nonextensive distribution, based on Tsallis’ statistics, is characterized by a dimensionless nonextensive parameter, q, and the results in the usual Boltzmann-Gibbs case are recovered when q→1. The thermodynamics of the linear sigma model and its corresponding phase diagram are analysed. At high temperature region, the critical temperature Tc is shown to decrease with increasing q from the phase diagram in the (T,μ) plane. However, larger values of q cause the rise of Tc at low temperature but high chemical potential. Moreover, it is found that μ different from zero corresponds to a first-order phase transition while μ=0 to a crossover one. The critical endpoint (CEP) carries higher chemical potential but lower temperature with q increasing due to the nonextensive effects.

scholarly journals Nonextensive statistical mechanics: a brief review of its present status

2002 ◽  
Vol 74 (3) ◽  
pp. 393-414 ◽  
Author(s):  
CONSTANTINO TSALLIS
Keyword(s):  
Statistical Mechanics ◽  
Long Range ◽  
Present Status ◽  
A Priori ◽  
Many Body ◽  
Nonextensive Statistical Mechanics ◽  
Physical Systems ◽  
Classical Systems ◽  
Low Dimensional ◽  
Entropic Index

We briefly review the present status of nonextensive statistical mechanics. We focus on (i) the central equations of the formalism, (ii) the most recent applications in physics and other sciences, (iii) the a priori determination (from microscopic dynamics) of the entropic index q for two important classes of physical systems, namely low-dimensional maps (both dissipative and conservative) and long-range interacting many-body hamiltonian classical systems.

A new structure entropy of complex networks based on nonextensive statistical mechanics

2016 ◽  
Vol 27 (10) ◽  
pp. 1650118 ◽  
Author(s):  
Qi Zhang ◽  
Meizhu Li ◽  
Yong Deng
Keyword(s):  
Statistical Mechanics ◽  
Complex Networks ◽  
Fundamental Problem ◽  
New Method ◽  
Nonextensive Statistical Mechanics ◽  
Index Set ◽  
Single Structure ◽  
Degree Structure ◽  
Structure Complexity ◽  
Entropic Index

The quantification of the complexity of network is a fundamental problem in the research of complex networks. There are many methods that have been proposed to solve this problem. Most of the existing methods are based on the Shannon entropy. In this paper, a new method which is based on the nonextensive statistical mechanics is proposed to quantify the complexity of complex network. On the other hand, most of the existing methods are based on a single structure factor, such as the degree of each node or the betweenness of each node. In the proposed method, both of the influence of the degree and betweenness are quantified. In the new method, the degree of each node is used as the constitution of the discrete probability distribution. The betweenness centrality is used as the entropic index q. The nodes which have big value of degree and betweenness will be have big influence on the quantification of network’s structure complexity. In order to describe the relationship between the nodes and the whole network more reasonable, a entropy index set is defined in this new method. Therefore, every node’s influence on the network structure will be quantified. When the value of all the elements in the entropic index set is equal to 1, the new structure entropy is degenerated to the degree entropy. It means that the betweenness of each node in the network is equal to each other. And the structure complexity of the network is determined by the node’s degree distribution. In other words, the new structure entropy is a generalization of the existing degree structure entropy of complex networks. The new structure entropy can be used to quantify the complexity of complex networks, especially for the networks which have a special structure.

Nonextensive statistical mechanics for robust physical parameter estimation: the role of entropic index

2021 ◽  
Vol 136 (3) ◽  
Author(s):  
João V. T. de Lima ◽  
Sérgio Luiz E. F. da Silva ◽  
João M. de Araújo ◽  
Gilberto Corso ◽  
Gustavo Z. dos Santos Lima
Keyword(s):  
Parameter Estimation ◽  
Statistical Mechanics ◽  
Physical Parameter ◽  
Nonextensive Statistical Mechanics ◽  
Entropic Index

Unbalance Response of a Dual Rotor System: Theory and Experiment

1993 ◽  
Vol 115 (4) ◽  
pp. 427-435 ◽  
Author(s):  
K. Gupta ◽  
K. D. Gupta ◽  
K. Athre
Keyword(s):  
System Theory ◽  
Transfer Matrix ◽  
Mode Shape ◽  
Reasonable Agreement ◽  
Complex Variables ◽  
Rotor System ◽  
Experimental Results ◽  
Unbalance Response ◽  
Theoretical Results ◽  
Theory And Experiment

A dual rotor rig is developed and is briefly discussed. The rig is capable of simulating dynamically the two spool aeroengine, though it does not physically resemble the actual aeroengine configuration. Critical speeds, mode shape, and unbalance response are determined experimentally. An extended transfer matrix procedure in complex variables is developed for obtaining unbalance response of dual rotor system. Experimental results obtained are compared with theoretical results and are found to be in reasonable agreement.

Laws of large numbers for q-dependent random variables and nonextensive statistical mechanics

2017 ◽  
Vol 31 (15) ◽  
pp. 1750117
Author(s):  
Marco A. S. Trindade
Keyword(s):  
Statistical Mechanics ◽  
Stochastic Processes ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Nonextensive Statistical Mechanics ◽  
Dependent Random Variables ◽  
Strong Law ◽  
Laws Of Large Numbers ◽  
Large Numbers

In this work, we prove a weak law and a strong law of large numbers through the concept of [Formula: see text]-product for dependent random variables, in the context of nonextensive statistical mechanics. Applications for the consistency of estimators are presented and connections with stochastic processes are discussed.

scholarly journals Nondistributive algebraic structures derived from nonextensive statistical mechanics

2008 ◽  
Vol 49 (9) ◽  
pp. 093509 ◽  
Author(s):  
Pedro G. S. Cardoso ◽  
Ernesto P. Borges ◽  
Thierry C. P. Lobão ◽  
Suani T. R. Pinho
Keyword(s):  
Statistical Mechanics ◽  
Algebraic Structures ◽  
Nonextensive Statistical Mechanics
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