## Index

## Description

In a general sense, Physics studies the laws of the Universe. This broad perspective can be reduced to say that Physics is concerned in the way in which objects move, that is everything which is subjected to the rules of

*Mechanics*. Nowadays, we know at least four different types of Mechanics which are called: Classical, Quantum, Relativistic and Statistical. Each Mechanic applies under a certain regime. Classical Mechanics deals with everyday objects, Quantum Mechanics with very little particles (like electrons), Relativistic Mechanics with very fast particles (whose velocity is close to the speed of light) and Statistical Mechanics with a big number of elements (of the order of the Avogadro's number). The theoretical description of these four Mechanics relies on the Hamiltonian formalism. Moreover, they can be used together, for instance, when the particles are very little and fast, Relativistic Quantum Mechanics is taken into account.**Statistical Mechanics**

When many agents are interacting together, they can give rise to peculiar behaviours which can't be reduced to the sum of the characteristics of the single elements making up the system. Such properties emerge as a collective behaviour of all the particles. These are called

*Complex Systems*. To grasp the concept intuitively, the following analogy is useful: the meaning of a word is not given by the sum of the meanings of each letters which make up the word, but it's the result of the "collective behaviour" of them. Again, in Physics, temperature is defined for a gas as a

*whole*and not for a

*single* particle. Thus, Statistical Mechanics can be considered as the mechanics underlying Complex Systems. Due to the high number of agents making up such systems, it is impossible, as well as not so interesting, to determine with arbitrary precision the behaviour of the system components. Indeed, a certain amount of uncertainty, that is of stochasticity or randomness, needs to be introduced in the mathematical formulation of the phenomenon, hence only averaged quantities can be observed. This is the origin of the adjective "Statistical" in the name of the subject.

Nowadays, the research trends in Statistical Mechanics can be divided in two branches: Non-equilibrium and Equilibrium. In the first case, the time evolution of the system is of main interest. Here, the most important quantity is the

*current*, that is the number of particles flowing in the system in a certain direction. Instead, Equilibrium Statistical Mechanics studies systems which have relaxed, that is when, in the long run, their current is null. In this case, the ability of the agents to assume the same value, called

*magnetisation*, against temperature is studied.

## Specific Topics

My research interests focus on both branches of Statistical Mechanics. In the following, you can find a brief description on the problems I'm working on.