Numbering Code	U-ENG29 39094 LJ57 U-ENG29 39094 LJ10	Year/Term	2022 ・ First semester
Number of Credits	2	Course Type	Lecture
Target Year		Target Student
Language	Japanese	Day/Period	Thu.2
Instructor name	UMENO KEN (Graduate School of Informatics Professor)
Outline and Purpose of the Course	Probability theory, statistical mechanics, and theory of stochastic processes are explained as methods to investigate systems with many degrees of freedom. Technics for describing dynamics, and fluctuation in equilibrium or stationary systems and some topics for nonequiliburium systems are explained.
Course Goals	To gain firmly the fundamental skills for understanding various phenomena with the use of probability theory and stochastic process.
Schedule and Contents	Fundamentals of probability and entropy,3times,Continuous and discrete stochastic variables are introduced and entropy, KL entropy and mutual information are explained. Fundamentals of statistical mechanics,3times,Fundamentals of thermodynamics are reviewed and statistical mechanics is formularized with the maximum entropy principle. Applications to ideal gases and spin systems are explained. Stochastic processes and random walks,3times,Stochastic processes, especially Markov processes are explained. As examples, Gauss process, Poisson process, Wiener process and random walks are explained. Langevin equaitons and Fokker-Planck equations,3times,Brownian motion is introduced as an example of Langevin equations. Derivation of Fokker-Planck equations from Langevin equations are described and several applications of both equations are explained. Some topics for nonequiliburium systems,2times,We explain some topics chosen from entropy production in relaxation processes from nonequiliburium states to equilibrium states, the linear responce theory, the fluctuation theory, thermal excitation, diffusion and so on.
Evaluation Methods and Policy	Based on quizzes and the semester final exam.
Course Requirements	Fundamentals of calculus and linear algebra
Study outside of Class (preparation and review)	Reviews through solving the assigned quizzes are expected.
Textbooks	Textbooks/References	None
References, etc.	To be announced in the lecture
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