Coarse-graining and symplectic non-squeezing

TL;DR

This paper explores the implications of the symplectic non-squeezing theorem for coarse-graining in classical statistical physics, linking geometric constraints to statistical hierarchies and phase space structures.

Contribution

It connects symplectic geometry, specifically the non-squeezing theorem, to coarse-graining and statistical physics, highlighting the role of Hofer's metric and phase space geometry.

Findings

Cubic cells in coarse-graining relate to Hofer's metric uniqueness.

Symplectic non-squeezing constrains coarse-graining procedures.

Implications for the BBGKY hierarchy are discussed.

Abstract

We address aspects of coarse-graining in classical Statistical Physics from the viewpoint of the symplectic non-squeezing theorem. We make some comments regarding the implications of the symplectic non-squeezing theorem for the BBGKY hierarchy. We also see the cubic cells appearing in coarse-graining as a direct consequence of the uniqueness of Hofer's metric on the group of Hamiltonian diffeomorphisms of the phase space.