Infopaket

Physical kinetics.

ОК13

Обов’язкова дисципліна для ОП

Second

2023/2024

4 Semester

6

Gaining knowledge about the abbreviated description of statistical systems, Bogolyubov's idea about the hierarchy of temporal relaxation processes, and the successive reduction of the description of non-equilibrium systems at different stages of time evolution. The ability to apply the principle of maximum entropy to obtain equilibrium and quasi-equilibrium distribution functions. Obtaining knowledge of the basic provisions of the theory of Brownian motion Ability to solve Langevin, Smoluchowski and Fokker-Planck equations for systems with one degree of freedom Ability to apply Langevin, Smoluchowski and Fokker-Planck equations in problems of chemical kinetics and molecular biology Obtaining knowledge of the basic provisions of the statistical theory of weakly non-equilibrium systems (theory of linear response to external mechanical disturbance, fluctuation-dissipative theorem)

Full-time form

1. Know and be able to apply the methods of mathematical analysis and linear algebra within the limits of the relevant courses taught at the Faculty of Physics. 2. To be able to solve ordinary linear differential equations. 3. To be able to solve linear differential equations in partial derivatives of the first order by the method of characteristics. 4. To know and be able to apply the Hamiltonian formalism of classical mechanics. 5. To know and be able to apply the methods of the mechanics of a continuous environment within the limits of the relevant courses taught at the Faculty of Physics. 6. Know and be able to apply the laws of equilibrium and non-equilibrium thermodynamics. 7. Know and be able to apply the methods of classical statistical mechanics of equilibrium systems.

As part of the "Physical Kinetics" course, statistical regularities of the main types of non-equilibrium systems (systems consisting of weakly interacting subsystems, weakly non-equilibrium systems) are considered. The goal of studying the discipline is to acquire systematic knowledge of the basic sections of non-equilibrium statistical physics (general provisions of non-equilibrium statistical physics, the theory of Brownian motion, the theory of linear response) and to master the relevant statistical methods of studying non-equilibrium systems. The educational task of the course consists in mastering the statistical methods of studying non-equilibrium systems

1. Evans D.J., Searles D., Williams S.R. Fundamentals of classical statistical thermodynamics:dissipation, relaxation and fluctuation theorems. – Wiley VCH, 2016. – 223 p. 2. Grigoriev A.M. Elements of statistical physics of non-equilibrium processes. - K.: "KPI print", 2019. - 137 p. 3. Kovacs R., Scarfone A.M., Abe S. Entropy and Non-Equilibrium Statistical Mechanics. – MDPI, 2020. – 118 p. 4. Freund J.A., Poschel Th. Stochastic Processes in Physics Chemistry and Biology. – Springer, 2010. – 499 p. 5. Sau Fa Kwok. Langevin and Fokker-Planck Equations and their Generalizations: Descriptions and Solutions. – WSPC, 2018. – 208 p. 6. Umarov S., Hahn M.G., Kobayashi K. Beyond the Triangle: Brownian Motion, Ito Calculus, and Fokker-Planck Equation - Fractional Generalizations. – World Scientific Publishing Company, 2018. – 192 p

The total volume is 90 hours, including: lectures – 30 hours; independent work - 60 hours

Student evaluation forms: - semester assessment: 1. Modular control work 1 (15 points-9 points). Doing homework (5 points-3 points). 2. Modular control work 2 (15 points-9 points). Doing homework (5 points-3 points). 3. Modular control work 3 (15 points-9 points). Doing homework (5 points-3 points). - final evaluation in the form of an exam A student is not admitted to the exam if he scored less than 36 points during the semester. The exam grade cannot be less than 24 points to receive an overall positive grade for the course.

Ukrainian