Irreversibility from staircases in symplectic embeddings

TL;DR

This paper explores how symplectic embedding results, specifically Fibonacci and Pell staircases, explain the emergence of macroscopic irreversibility in Hamiltonian systems with many degrees of freedom.

Contribution

It introduces a novel approach linking symplectic embedding flexibility and rigidity to the origin of irreversibility in complex Hamiltonian systems.

Findings

Symplectic staircases encode initial condition breadth.

Flexibility and rigidity results relate to irreversibility.

Framework connects symplectic geometry to thermodynamic behavior.

Abstract

We present an argument whose goal is to trace the origin of the macroscopically irreversible behavior of Hamitonian systems of many degrees of freedom. We use recent flexibility and rigidity results of symplectic embeddings, quantified via the (stabilized) Fibonacci and Pell staircases, to encode the underlying breadth of the possible initial conditions, which alongside the multitude of degrees of freeedom of the underlying system give rise to time-irreversibility.