PORTALE DELLA DIDATTICA

PORTALE DELLA DIDATTICA

PORTALE DELLA DIDATTICA

Elenco notifiche



Introduction to generalized statistical mechanics

01SCKKG

A.A. 2019/20

Course Language

Inglese

Degree programme(s)

Doctorate Research in Fisica - Torino

Course structure
Teaching Hours
Lecturers
Teacher Status SSD h.Les h.Ex h.Lab h.Tut Years teaching
Co-lectures
Espandi

Context
SSD CFU Activities Area context
*** N/A ***    
2018/19
PERIOD: OCTOBER - DECEMBER The course intends to introduce a series of advanced methodologies of statistical physics concerning nonlinear systems, both in equilibrium and in dynamic conditions. The techniques presented have a strong interdisciplinary character and is used to describe physical and non-physical (engineering, natural, social, economic, biological, etc.) complex systems. Particular emphasis is given to the physical paradigm for understanding the fundamental principles of the theory and at the same time some interdisciplinary applications are considered in order to highlight the versatility of the tools the course intends to provide.
A. NONLINEAR KINETICS 1. System evolution in the Fokker-Planck description 2. System evolution in the Boltzmann description 3. H-Theorem for non linear systems B. EQUILIBRIUM NON LINEAR SYSTEMS 1. Nonadditive entropy. Maximum entropy principle. 2. Thermodynamics of non linear systems (Legendre structure, thermodynamic and Lesche stability) C. POWER LAW TAILED DISTRIBUTIONS 1. Recalls of relativistic dynamics 2. Deformed exponential and associated deformed mathematics 3. Deformed entropy and the second law of thermodynamics 4. Statistical mechanics of the power law distributions D. NONEXTENSIVE STATISTICAL MECHANICS 1. The zoo of the entropies 2. The Student distribution and the Renie and Harvda-Charvat-Tsallis entropies 3. The nonextensive statistical mechanics and thermodynamics E. APPLICATIONS 1. Quantum statistics: anyons (Haldane-Wu), quons 2. The cosmic ray spectrum and the kappa-plasmas 3. Economic, financial and social systems. The Pareto law 4. Astrophysical systems 5. Quantum entanglement, Genomics, Complex networks
Exam:
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