Indeterminacy relations in random dynamics

TL;DR

This paper explores uncertainty measures in spatial diffusion processes, investigating the existence of complementary pairs with a positive lower bound on their joint dispersion, in a non-quantum context.

Contribution

It introduces a framework for understanding indeterminacy relations in classical stochastic dynamics, extending concepts typically associated with quantum mechanics.

Findings

Identifies conditions for the existence of uncertainty pairs in diffusion processes

Establishes lower bounds for joint dispersion measures in non-quantum systems

Provides insights into classical analogs of quantum uncertainty principles

Abstract

We analyze various uncertainty measures for spatial diffusion processes. In this manifestly non-quantum setting, we focus on the existence issue of complementary pairs whose joint dispersion measure has strictly positive lower bound.