The Continuity Equation Contains Non-Stochastic Motion

TL;DR

This paper demonstrates that the continuity equation inherently describes non-stochastic motion, showing that stochastic components become indistinguishable within this framework, thus clarifying its limitations and scope.

Contribution

It provides a theoretical characterization of the continuity equation, revealing that it inherently excludes stochastic motion components.

Findings

Continuity equation describes only non-stochastic motion.

Stochastic motion components are indistinguishable within the continuity equation.

The equation is equivalent to a system of first-order linear ODEs.

Abstract

The scientific question resolved by this paper is that the continuity equation appears as an equivalent language of the system of first-order linear ODE. The main result characterizes the fact that the continuity equation contains non-stochastic motion; a stochastic motion addressed by the continuity equation surely drops its stochastic part in a probabilistic indistinguishable manner.