PILLAR Course: Probability and Statistical Mechanics - Part 3: Some introductory topics in statistical mechanics

Thursday 9 Jan 2025, 08:30 → Thursday 27 Feb 2025, 10:30 Europe/Rome

Lecturers

Alessia Nota alessia.nota@gssi.it                                               

Stefano Olla stefano.olla@gssi.it

Lu Xu lu.xu@gssi.it

Timetable and workload

• Thursday, Jan 9th, 10:30-12:30
• Friday, Jan 10th, 10:30-12:30 & 14:30-16:30
• Monday, Jan 13th, 8:30-10:30
• Tuesday, Jan 14h, 10:30-12:30 & 14:30-16:30
• Monday, Jan 20th, 8:30-10:30
• Tuesday, Jan 21st, 10:30-12:30 & 14:30-16:30
• Monday, Jan 27th, 8:30-10:30
• Tuesday, Jan 28th, 10:30-12:30
• Thursday, Jan 30th, 8:30-10:30

 

Course content

Topic 1  - (Alessia Nota, Jan. 9th to 10th)

Topic 2 - (Stefano Olla, Jan. 13th to 21st)

Topic 3 - Hydrodynamics for asymmetric simple exclusion (Lu Xu, Jan. 27th to 30th)

Course description and outcomes

As a typical example of asymmetric attractive system, we study a nearest-neighbour simple exclusion process on periodic lattice with asymmetric jump probability. Different from the symmetric one, nontrivial evolution of the particle density can be observed under the hyperbolic space-time scale, following a quasi-linear conservation law. The key ingredient is an entropy inequality at microscopic level based on the attractiveness.

 

Course References

• Claude Kipnis, Claudio Landim: Scaling Limits of Interacting Particle Systems (Chapter 8. Hydrodynamic limit of asymmetric attractive processes).
• Josef Marek, etc.: Weak and Measure-valued Solutions to Evolutionary PDEs (Chapter 2. Scalar conservation laws).
• Fraydoun Rezakhanlou: Hydrodynamic limit for attractive particle systems on Z^d. Comm. Math. Phys. 140 417--448, 1991.
• Jozsef Fritz: Entropy pairs and compensated compactness for weakly asymmetric systems. Advanced Stuies in Pure Mathematics 39: Stochastic Analysis on Large Scale Interactive Systems, 143--171, 2004.