I will discuss a set of results on the classical mechanics of fractons - being defined as particles
whose dynamics obeys a consistent set of multipole conservation laws.  I will show that the nonlinear,
Machian, dynamics of the fractons is characterized by late-time attractors in position-velocity space,
despite the absence of attractors in phase space dictated by Liouville's theorem. These attractors violate
ergodicity and lead to non-equilibrium steady states, which always break translational symmetry, even
in spatial dimensions where the Hohenberg-Mermin-Wagner-Coleman theorem for equilibrium systems
forbids such breaking. While a full understanding of the many-body nonlinear problem is a formidable
and incomplete task, I will discuss progress towards a conceptual understanding of these results.
Altogether, these fracton systems host a new paradigm for Hamiltonian dynamics and non-equilibrium
many-body physics.

Joint work with Abhishodh Prakash, Alain Goriely and Ylias Sadki:

[2308.07372] Classical Non-Relativistic Fractons (arxiv.org)

[2312.02271] Machian fractons, Hamiltonian attractors and non-equilibrium steady states (arxiv.org)