In the first part of my lecture, I will discuss thermalization, ergodicity, and lack of them in classical systems. I will focus on paradigmatic example of spin glasses, and normal and anomalous diffusion processes. I will turn then to quantum closed systems, which, when perturbed or quenched, tend to “thermalize” in an ergodic way: the reduced density matrix of a block of the system is well...

Traditional Boltzmann-Gibbs statistical mechanics does not apply to systems with unstable interactions, because for such systems the conventional thermodynamic limit does not exist. In unstable systems the ground state energy does not have an additive lower bound, i.e. no lower bound linearly proportional to the number $N$ of particles or degrees of freedom. In this presentation (see [1] for...

As previously demonstrated, the entropy production – a standard measure of irreversibility of thermodynamic processes – is related to generation of correlations between degrees of freedom of the system and its environment [1]. A natural question appears whether such correlations are classical or quantum. This work deals with this problem by investigating noninteracting fermionic and bosonic...