Dipartimento di Scienze Statistiche

March 27, 2026, 12:00 In person.Room V (CU002) Webinar^.https://uniroma1.zoom.us/j/83625004899?pwd=bXCtz0 mp759PUh2lkqT0BUoVa0Uegg.1 Passcode: 123456 The Ehrenfest-Brillouin Model and its Applications Enrico Scalas Department of Statistical Sciences, Sapienza University of Rome The Ehrenfest-Brillouin Model (EBM) is a framework for understanding complex systems. We begin by establishing a hierarchy of state descriptions, moving from individual descriptions to statistical descriptions before arriving at "frequencies of frequencies." This structural approach facilitates a rigorous definition of the EBM as a random dynamic process whose state space coincides with these world descriptions. The EBM is an irreducible and aperiodic Markov chain, ensuring the convergence to a unique stationary distribution regardless of the initial state. The EBM dynamics incorporates interaction parameters that allow the system to recover Maxwell-Boltzmann, Bose-Einstein, or Fermi- Dirac statistics depending on the degree of dependency between agents. The model’s stochastic rules naturally yield emergent phenomena such as power laws. Finally, we discuss the broad applicability of the EBM in physics and the social sciences, for example in modeling wealth distribution. The EBM provides a unifying bridge between the combinatorial foundations of statistical mechanics and socio-economic theory.