Long-range interacting systems are systems in which the interaction potential decays slowly for large inter-particle distance. Typical examples of long-range interactions are the gravitational and Coulomb forces. The philosophical interest for studying these kinds of systems has to do with the fact that they exhibit properties that escape traditional definitions of equilibrium based on average ensembles. Some of those properties are ensemble inequivalence, negative specific heat, negative susceptibility and ergodicity breaking. Focusing on long-range interacting systems has thus the potential of leading one to an entirely different conception of equilibrium or, at least, to a revision of traditional definitions of it. But how should we define equilibrium for long-range interacting systems?
In this talk, I address this question and argue that the problem of defining equilibrium in terms of average ensembles is due to the lack of a time-scale in the statistical mechanical treatment. In consequence, I argue that adding a specific time-scale to the statistical treatment can give us a satisfactory definition of equilibrium in terms of metastable states. I point out that such a time-scale depends on the number of particles in the system, as it happens when phase transitions occur, also in the more usual context of short-range interacting systems like condensed matter ones. I thus discuss the analogies and the dissimilarities between the case of long-range systems and that of phase transitions and argue that these analogies, which should be interpreted as liberal formal analogies, can have an important heuristic role in the development of statistical mechanics for long range interacting systems.
Philosophy of Physics Seminar Convenors for MT19: Tushar Menon, Adam Caulton and Chris Timpson