Coarse Graining Reveals a Fluctuation-theorem-like Asymmetry in Financial Markets

Abstract

Fluctuation theorems show how coarse graining transforms microscopic symmetry into observable irreversibility. Here we ask whether an analogous symmetrybased diagnostic can be constructed for financial markets. At the microscopic level, each transaction pairs a buyer and a seller, whereas trading decisions are typically made from coarse-grained price histories. Using symmetric takeprofit and stop-loss rules, we compare the holding-time distributions of long and short trading ensembles generated from the same price series. Across equityindices, individual stocks and cryptocurrencies, the log-ratio of the two distributions shows a robust crossover. It remains nearly constant at short durations but becomes linear in the tail, implying an exponential directional asymmetry. The tail slope defines an effective market temperature, an operational measure of fluctuation intensity on the chosen observation scale. A Bachelier first-passage benchmark captures the exponential tails but not the asymmetry, because long and short positions share the same leading decay rate. By contrast, short-time correlations between overlapping positions provide a minimal mechanism for the asymmetry by generating direction-dependent subleading relaxation spectra in a coarse-grained Markov description. Together, these results establish a fluctuation-theorem-like diagnostic of irreversibility in financial markets and, more broadly, in complex systems accessible only through coarse-grained observables.