Derivation of Hamiltonian mechanics from determinism and reversibility

TL;DR

This paper demonstrates that Hamiltonian mechanics naturally arises from the principles of determinism and reversibility, connecting mathematical, thermodynamic, and informational perspectives.

Contribution

It provides a unified derivation of Hamilton's equations from multiple foundational viewpoints, emphasizing their fundamental link to determinism and reversibility.

Findings

Hamilton's equations align with deterministic and reversible evolution.

Multiple perspectives converge to support the derivation.

Generalization from single to multiple degrees of freedom.

Abstract

We put forth the idea that Hamilton's equations coincide with deterministic and reversible evolution. We explore the idea from five different perspectives (mathematics, measurements, thermodynamics, information theory and state mapping) and we show how they in the end coincide. We concentrate on a single degree of freedom at first, then generalize. We also discuss possible philosophical reasons why the laws of physics can only describe such processes, even if others must exist.