Nonequilibrium Thermodynamics and Statistical Physics (graduate level)
General Information
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Method: 2 hours lecture and 2 hours seminar per week
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Instructor: Dr. Sorinel Adrian Oprisan
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Prerequisite:
- Advanced Calculus (Ordinary and Partial Differential Equations)
- Equilibrium Thermodynamics and Statistical Physics (Classical and Quantum Ensemble Theory)
Course Description:
The goal is to learn the methods of nonequilibrium thermodynamics and to understand theirs statistical foundations. While the topic of nonequilibrium thermodynamics is very extensive, our focus will be on some very specific concepts. We will apply balance equations to fare-from-equilibrium processes in chemistry and biology. The central principle of Glansdorff and Prigogine for nonequilibrium processes is discussed in details and concrete examples are provided to prove its validity. Recent progresses in the field of non-extensive thermostatistis (Tsallis statistics) are discussed. In depth analyses of simple physical, chemical, and biological systems will be used to highlight the similarities and the major differences between the Gibbs and the new Tsallis statistics. The phenomenological understanding of the nonequilibrium processes is further strengthened by presenting a coherent statistical mechanism able to relate microscopic and macroscopic worlds.
Instructional Objectives:
At the end of the course, the students should be able to extract the balance equations for elementary physico-chemical processes, identify the entropy sources, obtain the steady solutions of nonlinear evolution equations, linearize them and analyze the stability of the steady solution(s). The students should be able to identify and solve simple stochastic equations in the framework of the Fokker-Planck theory. The students should be able to present their work both as a short (15 minutes) talk and in a written form.
Texts:
1. Glansdorff P., I. Prigogine, Thermodynamic theory of structure stability and fluctuations, Amsterdam, 1973.
2. Kreuzer H.J., Nonequilibrium Thermodynamics and Its Statistical Foundations, Clarendon, Oxford, 1981.
Topics:
1. Classical Thermodynamics of Far-from-Equilibrium Processes
1.1. Balance equations
1.2. Balance equations of mass, momentum, kinetic and potential energies
1.3. Balance equation of internal energy. Local formulation of the First Principle
1.4. Balance equation of entropy. The entropy source
1.5. Linear thermodynamics of far-from-equilibrium processes
1.5.1. Curier principle
1.5.2. Onsager relationships
1.5.3. Minimum entropy production theorem
1.5.4. Rayleigh-Benard effect
1.6. Nonlinear thermodynamics of far-from-equilibrium processes
1.6.1. Glansdorff-Prigogine evolution criterion
1.6.2. Applications
2. Extended thermodynamics of nonequilibrium thermodynamics
2.1. Generalized balance equations
2.2. Applications to transport phenomena
2.3. Statistical foundations of extended nonequilibrium thermodynamics
2.3.1. Grad solutions for extended entropy source equation
2.3.2. Statistical theory of fluctuations
2.3.3. Projection operator
2.3.4. Applications
3. Stochastic processes
3.1. Stochastic variables. Distributions and Correlations
3.2. Langevin stochastic equation
3.3 Fokker-Planck equation
3.4. Brownian motion. Wiener stochastic processes
3.5. Ornstein-Uhlenbeck stochastic processes. White noise
3.6. Applications
Evaluation and Grading
Homeworks: One homework every two weeks will be assigned. The purpose is to highlight special techniques presented during the lectures. The assignments may be both analytical and computational. The usual due date is usually after two weeks. Late homeworks are severely penalized (ten percent of the total grade each day). Academic dishonesty will not be tolerated.
Midterm Examinations: There are two written, in-class, partial examinations. There is one comprehensive final exam. No makeup exams. The exams are tentatively scheduled for ...
Project: A recent paper (less than five years) of your choice must be thoroughly understood and prepared for in-class presentation. The review papers may involve library search, web search, numerical algorithm implementation and testing, and slides preparation. Instead of a review paper you may present your graduate research results if they are related to our topics. However, it is expected that your in-class presentation will also be presentable at a national-level conference.
Grading: Final grade is th eweighted average with
Supplementary bibliography
  1. Arnold L., Stochastic Differential Equations: Theory and Applications, Wiley-Interscience, New York, 1974.
  2. Ignat M., Curs de termodinamica si fizica statistica, Ed. Univ. Al.I.Cuza Iasi, 1974.
  3. Jou D., Casas-Vazquez J., Lebon G., Extended irreversible thermodynamics, Springer-Verlag, Berlin, 1993..
  4. Keizer J., Statistical Thermodynamics of Nonequilibrium Processes, Springer-Verlag, New York, 1987.
  5. Muler I., T. Ruggeri, Extended Thermodynamics, Springer-Verlag, New York, 1993.
  6. Vīlcu R., A. Dobrescu, Termodinamica proceselor ireversibile, Ed. Tehnica, Bucuresti, 1982.
  7. Titeica S., Termodinamica, Ed. Academiei, Bucuresti, 1982.
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