In this course the knowledge of statistical physics is developed, with a particular attention to modern aspects involving interacting systems and critical phenomena, and applications to the physics of biological systems, in particular biopolymers, are discussed. To this end, a few basic elements of molecular biology are also introduced.

The student must acquire a deep knowledge of statistical physics and of its methodologies. The student must also acquire some basic elements of molecular biology and must learn to apply the techniques of statistical physics to some problems from the physics of biological systems, mainly in the field of biopolymers.

Mathematical analysis, general physics, quantum mechanics, probability theory.

1. Statistical physics Review: canonical and grand-canonical ensembles, non-interacting systems (10 hours). The Ising model: introduction and exact solutions in one dimension and on the fully connected graph (10 hours). Mean-field approximation (10 hours). Beyond mean-field approximation: Bethe-Peierls and belief propagation (5 hours). The two-dimensional Ising model: Peierls argument, low- and high-temperature expansions, free energy in zero field on a square lattice. The two-dimensional XY model at low temperatures (15 hours). An introduction to the real-space renormalization group (10 hours). 2. Elements of non-equilibrium statistical physics: free diffusion, diffusion under a thermodynamical potential, Kramers problem (20 hours). 3. Introduction to molecular biology The cell; small molecules; proteins and nucleic acids. (4 hours). 4. Statistical physics of biopolymers Stretching a single DNA molecule: experiments, the Freely Jointed Chain, the one-dimensional cooperative chain, the worm-like chain (8 hours). DNA melting: experiments, zipper model, Poland-Scheraga model (6 hours). The helix-coil transition. Polymer collapse: Flory's theory. Collapse of semiflexible polymers: lattice models and the tube model. The self-avoiding walk and the O(n) model. (6 hours). An introduction to protein folding and design. RNA folding and secondary structure. Protein and RNA mechanical unfolding (10 hours). Molecular motors (6 hours).

Frontal lectures, using mainly blackboard in block 1. Statistical physics, mainly slides in block 2. Introduction to molecular biology, and a mixture of both in block 3. Statistical physics of biopolymers. Problems are proposed after completing each topic and then solved after a few lectures, so that students have time to try and find their own solutions.

M. Plischke and B. Bergersen, Equilibrium statistical physics, World scientific R.K. Pathria and P.D. Beale, Statistical mechanics, Academic Press L. Peliti, Statistical mechanics in a nutshell, Bollati Boringhieri J.P. Sethna, Entropy, order parameters and complexity, Clarendon K. Sneppen and G. Zocchi, Physics in molecular biology, Cambridge P. Nelson, Biological Physics, Freeman B. Alberts et al, Molecular biology of the cell, Garland Lecture notes and slides will be provided.

Modalità di esame: Prova orale obbligatoria;

Exam: Compulsory oral exam;

... The exam is based on an oral tests, which can be splitted in two parts, one for block 1. Statistical Physics, and one for blocks 2. Introduction to molecular biology and 3. Statistical physics of biopolymers. In case of splitting, the final grade is the weighted average of the grades of each block. Each test typically involve questions on 2-3 topics, the first one being chosen by the student. The knowledge of statistical physics and its methodologies is tested by asking the student to derive proofs of the main results in block 1. The ability of the student to apply the techniques of statistical physics to problems from the physics of biological systems is tested by asking to discuss models of biopolymers and the relationship of their predictions to phenomenology.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.