Entropies and equilibria of many-particle systems:: An essay on recent research

This essay is intended to present a fruitful collaboration which has developed among a group of people whose names are listed above: entropy methods have proved over the last years to be an efficient tool for the understanding of the qualitative properties of physically sound models, for accurate numerics and for a more mathematical understanding of nonlinear PDEs. The goal of this essay is to sketch the historical development of the concept of entropy in connection with PDEs of continuum mechanics, to present recent results which have been obtained by the members of the group and to emphasize the most striking achievements of this research. The presentation is by no way an exhaustive review of the methods and results involving the entropy, not even in the field of PDEs. Many other researchers in and outside Europe have contributed to the development of this field, including - but not only - in collaboration with some of the people of the group. However, it can be claimed that this group had a leading role over the recent years and this essay is intended to explain how this occurred.