Probability Current
Chapter 21: Fokker-Planck and Distribution Dynamics — Continuity Equation & Probability Current $J$
From the book
Chapter 21: Fokker-Planck and Distribution Dynamics. In the chapter mind map this icon labels Continuity Equation & Probability Current $J$. The discussion below is excerpted and lightly edited from § Continuity Equation Perspective in Mathematics for AI and Machine Learning.
The Fokker–Planck equation can be written in continuity equation form:
where $\mathbf{J}_t(\mathbf{x})$ is the probability current (also called the probability flux):
What this drawing shows
What you see. Continuity equation in three beats: blue $J_{\mathrm{in}}$ enters first, $p$ accumulates in the control volume, then red $J_{\mathrm{out}}$ rises until flux balances.
In the mind map. Chapter 21 — Continuity Equation & Probability Current. See From the book above for definitions, figures, and worked examples.
Where to read next
Read the full definitions, figures, and worked examples in Chapter 21: Fokker-Planck and Distribution Dynamics — see the mind-map node Continuity Equation & Probability Current.