First real-data reading: a power market
840 hours of real day-ahead prices (CAISO SP15 hub, July 2026) put through the dissipation instruments. The finding survived four null classes, two adversarial reviews and one retraction — all on the public audit trail. Verdict: the day-ahead market is a measurably driven cycle, its irreversibility concentrated exactly where summer scarcity ramps drive it hardest.
Every week reads above its null median (the signal never changes sign); the statistical weight concentrates in the high-ramp second half — week 4 at 9.1× — exactly where the summer scarcity drive is strongest.
| observed pair-flux KLD | 0.0447 nats/h |
| reversible-null median | 0.0085 |
| reversible-null q99 | 0.0291 |
| verdict | driven cycle — detailed balance violated (p < 0.01) |
The null that matters: a reversible Markov chain with the data's own persistence (symmetrized pair flux). Spectral surrogates (FT, AAFT) are also computed and reported — the path through their failures, including one retraction, is finding F-0008/F-0009 in the open repository.
Prices are binned; each hour becomes a state (price level, direction of last move). A time-reversible market would cross each pair of states equally often in both directions. It doesn't: the daily loop — night valley, morning ramp, evening peak, decline — runs one way around, at about 1.1 nats of entropy production per day at hourly resolution. The same instrument, calibrated on games where the answer is provable (a road network reads exactly zero; rock–paper–scissors reads loudly), read this off a real market. Real-time 5-minute prices, by contrast, are genuinely at-null at this statistic — dwell dominates — and that contrast is part of the finding.