Faculty Research Perspectives

Statistical Mechanics of Cooperative Phenomena

Joel Lebowitz

Monday, February 2, 3:30 PM in Hill 705



Abstract.

Statistical mechanics tries to explain emergent cooperative phenomena in systems composed of very many identical or similar interacting individual entities. The entities studied can vary from atoms to cells to bacteria to fish to humans, but surprisingly many striking features of their collective behavior depend only on the nature of the interactions between them rather than on their intrinsic structure. Paradigms of such cooperative phenomena are phase transitions, which correspond to discontinuous changes in the properties or behavior of the aggregate system as some parameter is changed continuously. A common example is the change from solid to liquid or from liquid to gas, seen in all substances, as the temperature is varied---think in particular of the melting of ice and boiling of water at precisely 0 degrees and 100 degrees (at atmospheric pressure). Other examples include the development of traffic jams and the onset of epidemics in animal or human populations.

In this talk I will try to give a glimpse of the beautiful mathematical structure, involving probability, functional analysis, discrete mathematics, etc., developed during the past century to describe in a quantitative way many of these phenomena. (More information can be found in publications listed on my website: http://www.math.rutgers.edu/~lebowitz/)