Probability, typicality, and emergence in statistical mechanics

by Prof. Angelo Vulpiani (Sapienza Universita' di Roma)

Thursday Jan 22, 2026, 3:30 PM → 4:30 PM Europe/Rome

1/1-2 - Aula "C. Voci" (Dipartimento di Fisica e Astronomia - Edificio Marzolo)

The mathematical relevance of the probability theory for the statistical mechanics is obvious. From a physical and conceptual point of view the basic problem is the nature of the link between the probabilistic computations (i.e. the averages over an ensemble) and the actual results obtained in experiments which, a fortiori, are conducted on a single realisation (or sample) of the system under investigation.

I discuss  the basic features of  the  irreversibility at a macroscopic level and, thus, of the foundation of the second principle of thermodynamics as drawn by Boltzmann.

Emphasis will be put on the fact that, in systems characterized by a very large number of degrees of freedom, irreversibility is already manifested at a single-trajectory level for the vast majority of the far-from-equilibrium initial conditions, a property often referred to as typicality.