From Osher Doctorow

The generalized Lie derivative for a pair of real variables (x, y)
will be defined as:

1) L(x, y) = [x, y]* = xy + yx = 2xy

where the notation [x, y]* is used to contrast xy + yx with the more
common [x, y] = xy - yx used for ordinary Lie brackets with various
other types of arguments x, y.

Notice that in probability-statistics, xy is typically an indication
of "statistical independence", defined by:

2) P(AB) = P(A)P(B) = xy, x = P(A), y = P(B)

which is also equivalent to conditional probability P(B|A) = P(B)
since P(B|A) = P(AB)/P(A) and if the latter equals P(B) then we get
P(AB)/P(A) = P(B) or P(AB) = P(A)P(B), provided that P(A) is not 0.

But "statistical independence" is the WRONG direction of (Probable)
Causation/Influence, a fact which is easily remedied by examining:

3) L(x, x) = 2x^2, L(y, y) = 2y^2

This "Self-Independence" or "Self-Interaction" (depending on one's
viewpoint) is not at all decreased by multiplication by a second
variable, and so is arguably resembles x or y respectively in its role
in (Probable) Influence/Causation.

Thus, in the Riccati Differential Equation:

4) dy/dt = A(t) + B(t)y + C(t)y^2

we see that y and y^2 are respectively constant-interaction and self-
interaction, or constant-independence and self-independence types of
expressions:

5) L(y, 1) = 2y
6) L(y, y) = 2y^2

These resemble the roles of respectively momentum and energy with
regard to velocity/speed in classical physics and the limiting cases
of GR.

Osher Doctorow