Nonextensive Statistical Mechanics and Its ApplicationsSumiyoshi Abe, Yuko Okamoto Nonextensive statistical mechanics is now a rapidly growing field and a new stream in the research of the foundations of statistical mechanics. This generalization of the well-known Boltzmann--Gibbs theory enables the study of systems with long-range interactions, long-term memories or multi-fractal structures. This book consists of a set of self-contained lectures and includes additional contributions where some of the latest developments -- ranging from astro- to biophysics -- are covered. Addressing primarily graduate students and lecturers, this book will also be a useful reference for all researchers working in the field. |
Contents
HistoricalBac kground and Present Status | 3 |
II Quantum Density Matrix Description of Nonextensive Systems | 99 |
III Tsallis Theory the Maximum Entropy Principle and Evolution Equations | 157 |
IV ComputationalMetho ds for the Simulation of Classical and Quantum Many Body Systems Arising from Nonextensive Thermostatistics | 193 |
V Correlation Induced by Nonextensivity and the Zeroth Law of Thermodynamics | 234 |
VI Dynamic and Thermodynamic Stability of Nonextensive Systems | 243 |
Application to J Spin Glass Model | 253 |
VIII Protein Folding Simulations by a GeneralizedEnsemble Algorithm Based on Tsallis Statistics | 259 |
| 275 | |
Other editions - View all
Nonextensive Statistical Mechanics and Its Applications Sumiyoshi Abe,Yuko Okamoto Limited preview - 2008 |
Nonextensive Statistical Mechanics and Its Applications Sumiyoshi Abe,Yuko Okamoto No preview available - 2014 |
Nonextensive Statistical Mechanics and Its Applications Sumiyoshi Abe,Yuko Okamoto No preview available - 2010 |
Common terms and phrases
A. K. Rajagopal A. R. Plastino acceptance probability algorithm associated average Boltzmann Boltzmann-Gibbs Braz canonical ensemble Chem classical computational constant constraints corresponding d-dimensional defined density matrix depend derivative detailed balance discussed entangled entropy functional evolution exponential expression finite Fokker-Planck equation formalism free energy given Hamiltonian hence initial conditions integral interactions J. E. Straub Jaynes Lagrange multipliers Lett limit q linear maxent principle maximum entropy Molecular Dynamics Monte Carlo method Neumann non-extensive thermostatistics Nonextensive Statistical Mechanics nonlinear normalized q-mean value obtained operator optimization parameter particles partition function phase space Phys physical potential energy present probability distribution problem properties q-expectation values quantities quantum quantum entanglement R. S. Mendes sampling simulated annealing standard structure temperature theorem thermal thermodynamic Tsallis entropy Tsallis statistical unnormalized values of q zero