Irreversibility from staircases in symplectic embeddings

We present an argument whose goal is to trace the origin of the macroscopically irreversible behavior of Hamiltonian 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 freedom of the underlying system give rise to time-irreversibility.