Anno Accademico 2022/2023

  • Docente: Mirko Degli Esposti
  • Crediti formativi: 6
  • SSD: MAT/07
  • Lingua di insegnamento: Inglese
  • Modalità didattica: Convenzionale - Lezioni in presenza
  • Campus: Bologna
  • Corso: Laurea Magistrale in Physics (cod. 9245)

    Valido anche per Laurea Magistrale in Fisica del sistema Terra (cod. 8626)

Conoscenze e abilità da conseguire

At the end of the course the student will acquire the tools to build up dynamical models for the evolution of the classical physical systems formed by interacting particles under the influence of external fields. He/she will be able to use numerical techniques for the solution of the corresponding differential equation even in the case of fluctuating fields. In particular, in the limit of a large number of particles the kinetic and the fluid approximations will be developed; in the case of long range interactions the average field equations will be considered, together with self-consistent solutions and collision models based on stochastic processes.


Learning Outcomes (these substitute the previous OLD ones, they will become the new Learnoing Outcomes starting a.a. 23-24)

"By the end of the course, the student will have acquired the theoretical and numerical skills for the study of entropic properties of datasets, more or less structured.Theoretical skills will be acquired in the area of intersection between Complex Dynamical Systems Theory, Information Theory and Statistical Mechanics. Please refer to the syllabus for detailed topics.As far as numerical skills are concerned, the student will experiment with Python the numerical implementation of algorithms for the estimation of entropy, relative entropy and entropic production for stochastic processes on finite alphabets.Some applications in the area of natural language, gene sequences and (time permitting) in the area of human mobility data will be explored."

Entropic Information TheoryThis year the course will focus on developing the mathematical tools and properties around the concept of Entropy for Stochastic Systems, together with a discussion of some concrete applications to Natural Languages and Genomics.

Methods and Techniques lie in the intersection between Dynamical Systems, Statistical Mechanics and Information Theory.

It is a new Course, it will take place for the first time in the II semester, and detailed material is under construction.

The course will combine lectures at the blackboard with numerical investigations (in Python).

This online program will be refined over time, but here a first list of topics:

-Review of probability theory/dynamical systems.

-Shift spaces over finite alphabets.

-One-sided shifts. Examples.


-Two-sided shifts. Packings from coverings. Frequencies of finite blocks.

- Ergodicity and coverings.

- Entropy of a random variable.

- Entropic combinatorial bounds.

-Entropy on one-sided shifts.

- The Shannon-McMillan-Breiman (SMB) theorem. Examples

-One proof of SMB Theorem

-The Ornstein-Weissproof of the SMB theorem.

-First applications of the SMB theorem. Shannon’s source coding theorem.

-Entropy and coding–asymptotic optimality and Shannon’s theorem.

-Coding and Entropy.

-The Lempel-Ziv parsing and coding.

-Waiting times and entropy.

-Relative Entropy and Entropy Production

-Application to Genomics

-Application to Natural Languages

-Application to human mobility data


Here just the basic reference books used in the course. All sources, books and papers, will be available to students in digital format:

  • Shields, P.C. The Ergodic Theory of Discrete Sample Paths. Graduate Studies in Mathematics, AMS 1996.
  • Cover, M.T., and Thomas, A.J.: Elements of Information Theory. John Wiley & and Sons,1991.
  • Jakšic ́, V.: Lectures on entropy.I: Information-theoretic notions. Bahns et al (Eds): Dynami- cal Methods in Open Quantum Systems, Tutorials, Schools and Workshops in the Mathematical Sciences, (2019), 141-268, Springer

Metodi didattici

Lectures and Numerical Simulations (with Python)

Modalità di verifica e valutazione dell'apprendimento

to be defined

Strumenti a supporto della didattica

Blackboard and Python

Orario di ricevimento

Consulta il sito web di Mirko Degli Esposti