Editing Openai/693be8fb-8f0c-8010-93ea-5b83ef553357 (section)

=== 🔹 2. You apply your update rules ===

And you observe empirically:

: Every trajectory eventually flows into the zero matrix,
: and once at zero, no further evolution is possible.

This means your update rules are:
* dissipative (they reduce degrees of freedom),
* non-invertible (information is thrown away),
* entropy-decreasing with respect to your system’s internal measure.

This is fully compatible with your global linear constraint remaining exactly zero at every step.

In other words:

Constraint preserved  ≠  Entropy preserved.\text{Constraint preserved} \;\neq\; \text{Entropy preserved}.Constraint preserved=Entropy preserved.