Rey.BEng 28th September 2026
Wu, 2026. Von Neumann’s Two Quantum Entropies
arXiv:2609.30284
Tweet: https://x.com/IRFDMRG/status/2104433143164060011
Summary
Von Neumann wrote two entropies, both meant as thermodynamic entropy for quantum states.
- The familiar one.
S_27 = – Tr(rho ln rho)
Zero on every pure state.
Constant under unitary evolution.
It rises when you measure.
Wu’s claim: this is not thermodynamic entropy. Use it as a measure of entanglement.
- The forgotten one. Wigner–von Neumann.
S_29 = – sum p_i ln p_i
The p_i come from coarse-graining the state over phase space cut into Planck cells.
Nonzero on almost all pure states.
Extensive.
It can rise in irreversible processes such as diffusion, even when no measurement is written.
Von Neumann already said the 1927 expression was computed as if the observer could carry out every measurement possible in principle. That is not the thermodynamic observer. The 1929 form is the one he kept for ordinary mechanical evolution, where the observer does not know everything that is measurable.
Six pages. Statistical mechanics plus quantum. No Ace vocabulary. The link is the split.
Synthesis
Ace entropy is not dimensionless first.
It lives on the Instant band.
Centroid: m^4
Entropy limit: S = phi^{m(4)}
Working unit: Sm^4
Sm^4 is entropy times the fourth length.
S^4 volume element goes as pi^2 r^4.
That is why the letter carries m^4 and not a bare count.
Two clocks, already on the sheet.
Trigger
E = c^2 (m)
1st and 2nd moment. Start and finish.
Action!
Fire = m^sigma_m/s2
Top and bottom rows of the flow cell.
Work in Moments 3 and 4.
Wu’s two formulae sit on those two clocks.
S_27 is the Observational mark when the observer is allowed every measurement.
Pure state. Zero leftover on that clock.
That is Station II: the void after (f) is skipped, or after (f) is granted in full.
Entanglement is the correlation left when the face is read as if nothing were hidden.
Ace does not need a new name for that. It is the Born face. P = |psi|^2.
S_29 is thermodynamic because the cell is coarse.
Planck cells are a construct partition of the patch.
The observer does not take every measurement.
Entropy can rise while the fine state stays pure.
That is Action! on the wall.
sigma is the leftover the first stroke does not cancel.
Sm^4 is that leftover given volume at the centroid.
So:
S_27 entanglement / fine face Station II
S_29 thermodynamic / coarse cell Stations VII–VIII, then XII
Sm^4 Ace unit of the coarse cell Instant, m^4
The paper does not derive Sm^4.
It returns a thermodynamic entropy that is allowed to be nonzero on a pure state.
That is the door back into physics.
A pure wavefunction can still carry a patch leftover.
The leftover has units.
On the twelve stations
II Measurement
S_27 is the postulated mark when everything measurable is granted.
(f) is the hold. Skip it and you only have S_27.
VII Moment 3
Action! enters.
Coarse grain begins. Bending. m^4 torque.
VIII Moment 4
Flow cell closes.
S_29 can rise in diffusion without a measurement line.
Grip or slip. sigma_R = 2- = 1.999…
IX Black-hole information
S_27 on a pure global state is zero. The paradox is written on that clock.
S_29 on a coarse horizon cell need not be zero.
Thin-wall ring keeps the leftover. T_H stays Observational.
XII Dark energy
10^120 is a frozen first stroke against a live patch.
Sm^4 at the centroid is the Ace name for the live patch.
Not a new fluid.
What this does not claim
Wu does not prove Ace.
Ace does not replace -Tr(rho ln rho) in quantum information.
Planck cells in 1929 are not Lewe’s contact patch, though both are coarse faces.
Sm^4 is not SI-homogeneous with joule per kelvin until the fourth length is read as Instant centroid, not as a spare metre.
The link is the forgotten permission:
thermodynamic entropy may sit on a state that looks pure on the fine clock.
That is enough to bring entropy back into the drawing
without converting Fire into a new c.
Lettering
Trigger E = c^2 (m)
Action! Fire = m^sigma_m/s2
Entropy S = phi^{m(4)}
Unit Sm^4
S_27 entanglement face fine
S_29 thermodynamic face coarse
sigma king unit on the ring
Draw first. Calculate second.
K off the wall.
Paper
https://arxiv.org/abs/2609.30284
Meg3
https://ace-consultancy.uk/meg3-rest-time-dimensional-unit-assignment/
Mef
https://ace-consultancy.uk/mef-walkthrough-construction/
Ace Consultancy — Reality Engineers
Coefficient-free living for life.
