The diffusion equation and the principle of minimum Fisher information

TL;DR

This paper demonstrates that the diffusion equation and its adjoint can be derived using an information-theoretic approach centered on the principle of minimum Fisher information, with minimal assumptions.

Contribution

It introduces a novel derivation of the diffusion equation based solely on the principle of minimum Fisher information, highlighting an information-theoretic foundation.

Findings

Diffusion and adjoint equations derived from Fisher information principle

Minimal assumptions needed for derivation

Supports information-theoretic approach to diffusion processes

Abstract

It is shown that the diffusion equation and its adjoint (time reversed) equation can be derived with only a few assumptions, using an information-theoretic approach based on the principle of minimum Fisher information