Statistical Mechanics of Systems with Long-Range Interactions

Systems with long-range forces behave very differently from those in which particles interact
through short-range potentials.
For systems with short-range interactions, for arbitrary initial conditions,
the final stationary state corresponds to the thermodynamic equilibrium
and can be described equivalently by either a microcanonical, canonical, or a grand-canonical ensemble.
On the other hand, for systems with unscreened long-range forces, equivalence between
ensembles breaks down. Isolated long-range interacting systems --- in
thermodynamic limit --- do not evolve
to the usual Maxwell-Boltzmann equilibrium, but become trapped in a
non-ergodic stationary state which explicitly depends on the initial particle distribution.
In this talk, a theoretical framework will be presented which allows us to
predict
the final stationary state to which a long-range interactioning system will evolve.
The theory is able to
quantitatively account for both density and
velocity distributions in the stationary state,
without any adjustable parameters [1,2,3].\\

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[1] Y. Levin, R. Pakter and T. N. Telles, Phys. Rev. Lett. {\bf 100}, 040604 (2008).\\
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[3] R. Pakter, and Y. Levin, Phys. Rev. Lett. {\bf 106}, 200603 (2011);
F. P. da C. Benetti, T. N. Teles, R. Pakter, and Y. Levin,
Phys. Rev. Lett. {\bf 108}, 140601 (2012);
T. N. Teles, F. P. da C. Benetti, R. Pakter, and Y. Levin,
Phys.Rev. Lett. {\bf 109}, 230601 (2012);
R. Pakter, B. Marcos, and Y. Levin, Phys. Rev. Lett. {\bf 111}, 230603 (2013).F. P. C. Benetti, A. C. Ribeiro-Teixeira, R. Pakter, and Y. Levin, Phys. Rev. Lett. { \bf 113}, 100602 (2014).
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[3] Y. Levin et al., Phys. Rep. { \bf 535}, 1 (2014).