Abstract

Long-range interacting systems (LRI) 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 stationary probability distributions. How should we define equilibrium for LRI then? In this contribution, we argue that a comparison with ergodicity-breaking phase transitions gives us a qualitative understanding of equilibrium for these kinds of systems in terms of metastable equilibria. As in the case of phase transitions, we contend that in LRI one could account for metastable equilibria by defining the dynamics for finite-time scales. However, in contrast to phase transitions, we show that these metastable states depend on unknown initial conditions and do not correspond to Boltzmannian equilibrium. This negative conclusion provides a possible basis for future scientific research.