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.

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.

ENTROPIC REPULSION BETWEEN FLUCTUATING SURFACES

1990 ◽  
Vol 04 (11n12) ◽  
pp. 1763-1808 ◽  
Author(s):  
W. JANKE
Keyword(s):  
Monte Carlo ◽  
Simple Model ◽  
Statistical Mechanics ◽  
Monte Carlo Simulations ◽  
Long Range ◽  
Entropic Repulsion ◽  
Physical Systems ◽  
Model Surfaces ◽  
Out Of Plane ◽  
Repulsive Forces

The statistical mechanics of fluctuating surfaces plays an important role in a variety of physical systems, ranging from biological membranes to world sheets of strings in theories of fundamental interactions. In many applications it is a good approximation to assume that the surfaces possess no tension. Their statistical properties are then governed by curvature energies only, which allow for gigantic out-of-plane undulations. These fluctuations are the “entropic” origin of long-range repulsive forces in layered surface systems. Theoretical estimates of these forces for simple model surfaces are surveyed and compared with recent Monte Carlo simulations.

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

Many body dynamics

2018 ◽  
Author(s):  
Joseph F. Boudreau ◽  
Eric S. Swanson
Keyword(s):  
Statistical Mechanics ◽  
Body Problem ◽  
Many Body ◽  
Complex Objects ◽  
Constrained Dynamics ◽  
Gravitational Systems ◽  
Body Dynamics ◽  
System Temperature ◽  
Speed Up ◽  
Gravitating Systems

Specialized techniques for solving the classical many-body problem are explored in the context of simple gases, more complicated gases, and gravitating systems. The chapter starts with a brief review of some important concepts from statistical mechanics and then introduces the classic Verlet method for obtaining the dynamics of many simple particles. The practical problems of setting the system temperature and measuring observables are discussed. The issues associated with simulating systems of complex objects form the next topic. One approach is to implement constrained dynamics, which can be done elegantly with iterative methods. Gravitational systems are introduced next with stress on techniques that are applicable to systems of different scales and to problems with long range forces. A description of the recursive Barnes-Hut algorithm and particle-mesh methods that speed up force calculations close out the chapter.

scholarly journals Machine Learning for Statistical Modeling

2021 ◽  
Vol 26 (3) ◽  
pp. 1-17
Author(s):  
Urmimala Roy ◽  
Tanmoy Pramanik ◽  
Subhendu Roy ◽  
Avhishek Chatterjee ◽  
Leonard F. Register ◽  
...  
Keyword(s):  
Machine Learning ◽  
Time Distribution ◽  
Switching Time ◽  
A Priori ◽  
Random Access ◽  
Spin Transfer Torque ◽  
Support Vector ◽  
Micromagnetic Simulations ◽  
Physical Systems ◽  
Computational Resources

We propose a methodology to perform process variation-aware device and circuit design using fully physics-based simulations within limited computational resources, without developing a compact model. Machine learning (ML), specifically a support vector regression (SVR) model, has been used. The SVR model has been trained using a dataset of devices simulated a priori, and the accuracy of prediction by the trained SVR model has been demonstrated. To produce a switching time distribution from the trained ML model, we only had to generate the dataset to train and validate the model, which needed ∼500 hours of computation. On the other hand, if 10 6 samples were to be simulated using the same computation resources to generate a switching time distribution from micromagnetic simulations, it would have taken ∼250 days. Spin-transfer-torque random access memory (STTRAM) has been used to demonstrate the method. However, different physical systems may be considered, different ML models can be used for different physical systems and/or different device parameter sets, and similar ends could be achieved by training the ML model using measured device data.

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