Although there is not a complete “proof” of the second law of thermodynamics based on microscopic dynamics, two properties of Hamiltonian systems have been used to prove the impossibility of work extraction from a single thermal reservoir: Liouville’s theorem and the adiabatic invariance of the volume enclosed by an energy shell (Helmholtz's theorem). In this talk, I will review these two...

We show that the entropy production in small open systems coupled to environments made of extended baths is predominantly caused by the displacement of the environment from equilibrium rather than, as often assumed, the mutual information between the system and the environment. The latter contribution is strongly bounded from above by the Araki-Lieb inequality, and therefore is not...

Transitions to chaos have been previously extensively studied in different setups of randomly connected networks. The prevailing assumption is that, due to the central limit theorem, synaptic input can be modeled as a Gaussian random variable. In this scenario, a continuous transition has been found in rate models with smooth activation functions. However, these models do not take into account...

A $q$-neighbor majority-vote model for the opinion formation is introduced in which agents

represented by two-state spins update their opinions on the basis of the opinions of

randomly chosen subsets of $q$ their neighbors ($q$-lobbies). The agents with probability

$(1-2p)$, $0\le p\le1/2$, obey the majority-vote

rule in which the probability of the opinion flip depends only on the sign of...