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Introduction to generalized statistical mechanics

01SCKKG

A.A. 2019/20

Course Language

Inglese

Course degree

Doctorate Research in Fisica - Torino

Course structure
Teaching Hours
Teachers
Teacher Status SSD h.Les h.Ex h.Lab h.Tut Years teaching
Teaching assistant
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.
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
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
ModalitÓ di esame:
Exam:
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Exam:
In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.
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