Pedro W. Lamberti

We investigate the dynamics of a two-dimensional Sznajd model in which a third ideological position emerges spontaneously from local interactions between agents. Starting from random initial conditions, we observe that this emergent position arises solely as a result of the interaction dynamics, and not from predefined agent states. We analyze the system's behavior as a function of social apathy, modeled as the fraction of nonparticipating agents, and identify a critical apathy threshold that separates distinct regimes of opinion dominance. To quantify the interplay between disorder and structure in the system, we employ the complexity-entropy plane. This analysis reveals that the system is robust to asymmetries in initial conditions; its macroscopic behavior remains qualitatively unchanged. Furthermore, we find that statistical complexity reaches a maximum near the transition region, highlighting the emergence of rich collective dynamics characterized by abrupt topological changes parametrized by apathy.

We investigate bounds in the transmission of classical information through quantum systems. Our focus lies in the generalized Holevo theorem, which provides a single-letter Holevo-like inequality from arbitrary quantum distance measures. Through the introduction of the [ ]-[ ]-Rényi relative entropies, which comprise known relevant quantities such as the Rényi relative entropy and the sandwiched Rényi relative entropy, we establish the Holevo–Rényi inequality. This result leads to a quantum bound for the [ ]-mutual information, suggesting new insights into communication channel performance and the fundamental limits for reliability functions in memoryless multi-letter communication channels.