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 fluid dynamics and molecular biology are also introduced.

The student must acquire a deep knowledge of statistical physics, of its methodologies and its relationships with information theory. The student must also acquire some basic elements of fluid dynamics and 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 (6 credits)
Partition function, free energy, entropy.
Ideal systems. Interacting systems: Ising model and phase transition. Approximate methods for interacting systems: mean field and generalizations, Bethe-Peierls and belief propagation.
Low and high temperature expansions, duality. Free energy of the two-dimensional Ising model.
The XY model in 2 dimensions.
Introduction to the position space renormalization group.

2. Introduction to continuum and fluid mechanics (1.5 credits)
Kinematics of a continuum body (Lagrangian and Eulerian descriptions, rigid motion, Reynolds' transport theorem), dynamics of a continuum body (principle of mass conservation, principle of conservation of linear and angular momentum, Cauchy's stress theorem and stress tensors), fluid mechanics (constitutive assumptions of ideal and viscous fluids, Reynolds' number, solutions of Navier-Stokes equations in simple situations).

3. Introduction to molecular biology (0.5 credits)
The cell; small molecules; proteins and nucleic acids.

4. Statistical physics of biopolymers (4 credits)
Stretching a single DNA molecule: experiments, the Freely Jointed Chain, the one-dimensional cooperative chain, the worm-like chain.
DNA melting: experiments, zipper model, Poland-Scheraga model.
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.
An introduction to protein folding and design. RNA folding and secondary structure. Protein and RNA mechanical unfolding.
Molecular motors.

Frontal lectures, using mainly blackboard in blocks 1. Statistical physics and 2. Introduction to continuum and fluid mechanics, mainly slides in block 3. Introduction to molecular biology, and a mixture of both in block 4. 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.

The exam is based on an oral tests, which can be splitted in up to three parts, one for block 1. Statistical Physics, one for block 2. Introduction to continuum and fluid mechanics and one for blocks 3. Introduction to molecular biology and 4. 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.