About the maximum entropy principle in non equilibrium statistical mechanics

The maximum entropy principle (MEP) apparently allows us to derive, or justify, fundamental results of equilibrium statistical mechanics. Because of this, a school of thought considers the MEP as a powerful and elegant way to make predictions in physics and other disciplines, which constitutes an alternative and more general method than the traditional ones of statistical mechanics. Actually, careful inspection shows that such a success is due to a series of fortunate facts that characterize the physics of equilibrium systems, but which are absent in situations not described by Hamiltonian dynamics, or generically in nonequilibrium phenomena. Here we discuss several important examples in non equilibrium statistical mechanics, in which the MEP leads to incorrect predictions, proving that it does not have a predictive nature. We conclude that, in these paradigmatic examples, the "traditional" methods based on a detailed analysis of the relevant dynamics cannot be avoided

Metastability of Logit Dynamics for Coordination Games

Logit Dynamics [Blume, Games and Economic Behavior, 1993] are randomized best response dynamics for strategic games: at every time step a player is selected uniformly at random and she chooses a new strategy according to a probability distribution biased toward strategies promising higher payoffs. This process defines an ergodic Markov chain, over the set of strategy profiles of the game, whose unique stationary distribution is the long-term equilibrium concept for the game. However, when the mixing time of the chain is large (e.g., exponential in the number of players), the stationary distribution loses its appeal as equilibrium concept, and the transient phase of the Markov chain becomes important. It can happen that the chain is "metastable", i.e., on a time-scale shorter than the mixing time, it stays close to some probability distribution over the state space, while in a time-scale multiple of the mixing time it jumps from one distribution to another. In this paper we give a quantitative definition of "metastable probability distributions" for a Markov chain and we study the metastability of the logit dynamics for some classes of coordination games. We first consider a pure $n$-player coordination game that highlights the distinctive features of our metastability notion based on distributions. Then, we study coordination games on the clique without a risk-dominant strategy (which are equivalent to the well-known Glauber dynamics for the Curie-Weiss model) and coordination games on a ring (both with and without risk-dominant strategy)

La prova scientifica: diritto, epistemologia, strumenti d’acquisizione

SOMMARIO: 1. IL PROCESSO COME MODELLO EPISTEMICO?-; 2. I LIMITI NORMATIVI ATTUALI A UNA DISCIPLINA EPISTEMICA DEL PROCESSO-; 3. IL PROCESSO CIVILE DAVANTI ALL’A.G. E IL NECESSARIO FONDAMENTO SOCIALE DELLA DECISIONE-; 4. LE FONTI ESPERTE COME FATTORE DEL DUE PROCESS E DI SOCIAL EPISTEMOLOGY -; 5. IL PRIMATO DELLA DEMOCRAZIA SULLA TECNOCRAZIA-; 6. IL PECULIARE METODO SCIENTIFICO DEL PROCESSO: IL CONTRADDITTORIO-; 7. (SEGUE): IL VALORE DEL CONTRADDITTORIO ANCHE PRESSO IL GIUDICE SPECIALIZZATO-; 8. STRUMENTI DI ACQUISIZIONE DELLA PROVA SCIENTIFICA NELL’ESPERIENZA DEGLI ORDINAMENTI DI CIVIL LAW E DI COMMON LAW: REVISIONI STORICHE, EVOLUZIONI RECENTI E IBRIDAZIONI RECIPROCHE-; 9. IL CONTRADDITTORIO CON (E NON SOLTANTO TRA) LE PARTI SULLA SCELTA DELLA FONTE ESPERT

A new quantitative approach to the normativity of the judicial precedent

Ricerca sui fattori normativi misurabili della decisione giudiziari