Non-Equilibrium Thermodynamics of Cryptocurrency Perpetual Futures: Jarzynski Equality, Regime Classification, and Physics-Informed Trading

We establish a mapping between non-equilibrium statistical mechanics and cryptocurrency perpetual futures markets, where the funding rate mechanism acts as an external thermodynamic driving force on the basis (perpetual–spot price difference). Modeling the basis as an overdamped Langevin particle in a harmonic potential, we define thermodynamic quantities—energy, work, free energy, temperature, and entropy production—directly from market observables. We test the Jarzynski equality (JE) and the detailed fluctuation theorem (DFT) on 6.2 years of Binance data (January 2020–March 2026) across three assets: BTC, ETH, and SOL (19,697 funding cycles, 156,896 hourly basis observations). Key findings: - The JE holds to within 2.0% for BTC and 3.2% for ETH (first-ever test on financial data) - Basis relaxation time τ = 1/κ predicts JE validity — a novel, testable prediction - The second law holds for BTC/ETH but is violated for SOL (non-equilibrium steady state) - 4 physics-derived trading signals significantly outperform naive funding arbitrage (p < 0.05) Full codebase (Python, DuckDB) and LaTeX source included. All trading results use virtual money only.