A Modern Introduction to Nonequilibrium Statistical Mechanics (E)

This is a full-fledged introductory lecture on nonequilibrium statistical mechanics, targeting graduate and motivated undergraduate students in physics. It is based on my lectures at Gakushuin University in 2021 and 2023.

The lecture aims to present the fundamental concepts and results of nonequilibrium statistical mechanics from a "modern" perspective, striving to convey them as clearly as possible. For example, the lecture starts with the Jarzynski equality and the "fluctuation theorem", and concludes with Einstein's theory of Brownian motion. This is strictly the opposite of typical lectures or textbooks. But I believe our approach is logically straightforward, and I hope it is easily understandable. Please note that the focus is purely on theory (or rather, mathematical aspects), and applications are not discussed. (Sorry!) Please refer to the orientation ( YouTube (09:54)) for more details.

There is a Japanese version of the same course.

Lecture videos and slides

Part 1: Foundation (slides, pdf 8.5MB)

1-1 Classical Hamiltonian Mechanics (pp.1-12) / YouTube (34:34)
1-2 Jarzynski equality and the second law of thermodynamics (pp.13-19) / YouTube (17:19)
1-3 Heat conduction and the fluctuation theorem (pp.20-25) / YouTube (17:20)
1-4 Detailed balance conditions for effective stochastic processes (pp.26-40) / YouTube (44:44)
1-5 References / YouTube (04:08)

Part 2: Abstract theory (slides, pdf 10MB, revised: July 26, 2023)

2-1 Probability (pp.1--10) / YouTube (25:21, revised: July 26, 2023)
2-2 Entropy (pp.11-17) / YouTube (14:42)
2-3 Stochastic matrix and basic convergence theorem (pp.18--27) / YouTube (33:32)
2-4 Markov jump processes (pp.28--38) / YouTube (40:35, revised: July 26, 2023)
2-5 Description in terms of paths (pp.39--42) / YouTube (18:53)
2-6 Expectation values and their relations (pp.43--46) / YouTube (17:57)
2-7 Abstract fluctuation theorems for Markov jump processes (pp.47--51) / YouTube (22:36)
2-8 References / YouTube (01:25)

Part 3: Nonequilibrium processes in an equilibrium environment (slides, pdf 4.9MB)

3-1 Relaxation process in an equilibrium environment (pp.1--6) / YouTube (24:33)
3-2 Jarzynski equality (pp.7--15) / YouTube (28:04)
3-3 No pumping theorem (pp.16--21) / YouTube (22:54)
3-4 References / YouTube (02:22)

Part 4: Nonequilibrium states and processes in nonequilibrium environments (slides, pdf 8.2MB)

4-1 Relaxation to nonequilibrium steady states (NESS) (pp.1--5) / YouTube (22:05)
4-2 Liner response relations (pp.6--14) / YouTube (41:42)
4-3 Reciprocal relations (pp. 15--18) / YouTube (15:09)
4-4 Improved Shiraishi-Saito inequality (pp.19--25) / YouTube (19:19)
4-5 No free pumping theorem (pp.26--28) / YouTube (08:10)
4-6 Trade-off relation between power and efficiency of a heat engine (pp.29--37) / YouTube (28:01)
4-7 References / YouTube (02:05)

Part 5: The theory of Brownian motion (slides, pdf 4.6MB)

5-1 Typical Experiment, Kramers equation (pp.1--8) / YouTube (30:37)
5-2 Langevin equation (pp.9--14) / YouTube (16:50)
5-3 Einstein's theory of Brownian motion, References, Goodbye! (pp.15--20) / YouTube (21:09)

Hal Tasaki "A Modern Introduction to Nonequilibrium Statistical Mechanics"

Lecture videos and slides