Testing detailed balance in daily cryptocurrency markets: irreversibility in range–volume dynamics, and none detectable in candlestick shape

A non-equilibrium steady state is marked by broken detailed balance: probability circulates in state space, and the dynamics acquires an arrow of time. We test for this signature in daily cryptocurrency markets using only open–high–low–close–volume bars for 22 USDT-quoted pairs from one venue. Reversibility is assessed on transition counts rather than through the plug-in entropy production rate, whose finite-size bias consumes most of its power, and two corrections prove necessary. The count statistic’s degrees of freedom are the cyclomatic number of the realized support graph, not the number of state pairs, because Kirchhoff’s current law constrains the pair asymmetries; the pair count delivers a nominal 5% test at 0.2%. Block-permutation surrogates are invalid for this statistic, since a block of length L leaves a fraction ( L − 1 ) / L of transitions in their original order. No violation of first-order detailed balance is detected for the candlestick shape in any of 44 tests, which bounds any violation rather than evidencing a reversible mechanism, and follows largely from the near-absence of first-order dependence. Range–volume dynamics differ: with the state space selected on memory using five design assets that are then set aside, the bar range and traded volume jointly reject detailed balance in 12 of 17 held-out assets, with excess asymmetry positive in all 17 and median informational entropy production of 1.9 × 1 0 − 2 nats per bar, significant in 13. The finding survives an alternative partition, a parametric reversible null, and a control isolating the backward-looking normalization; persistence alone does not reproduce it.