https://doi.org/10.1140/epjst/e2017-70064-x
Regular Article
On the relevance of the maximum entropy principle in non-equilibrium statistical mechanics
1 University of Cassino, 03043 Cassino, Italy
2 Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
3 INFN, Sezione di Torino, Via Pietro Giuria 1, 10125 Torino, Italy
4 Kavli Institute for Theoretical Physics China, CAS, Beijing 100190, P.R. China
5 Università di Roma “Sapienza”, Dipartimento di Fisica, Rome, Italy
6 CNR, Istituto Sistemi Complessi, P.le A. Moro 2, 00185 Rome, Italy
a e-mail: gennaro.auletta@gmail.com
b e-mail: lamberto.rondoni@polito.it
c e-mail: Angelo.Vulpiani@roma1.infn.it
Received: 1 March 2017
Published online: 19 April 2017
At first glance, the maximum entropy principle (MEP) apparently allows us to derive, or justify in a simple way, 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, rather than a useful technical tool like others in statistical physics. From this point of view the MEP appears as an alternative and more general predictive method than the traditional ones of statistical physics. 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, an approach that uses a detailed analysis of the relevant aspects of the dynamics cannot be avoided.
© EDP Sciences, Springer-Verlag, 2017
