Entropic Dynamics: from Entropy and Information Geometry to Hamiltonians and Quantum Mechanics

TL;DR

This paper derives quantum mechanics from entropic inference methods, showing how Hamiltonian dynamics and the quantum potential naturally emerge from information geometry without relying on an action principle.

Contribution

It demonstrates that Hamiltonian dynamics and the quantum potential can be derived within entropic dynamics using information geometry, offering a new perspective on quantum theory's foundations.

Findings

Hamiltonian dynamics arise as non-dissipative entropic dynamics.

Quantum potential form follows from information geometry.

Quantum theory can be derived without an action principle.

Abstract

Entropic Dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. There is no underlying action principle. Instead, the dynamics is driven by entropy subject to the appropriate constraints. In this paper we show how a Hamiltonian dynamics arises as a type of non-dissipative entropic dynamics. We also show that the particular form of the "quantum potential" that leads to the Schroedinger equation follows naturally from information geometry.