Jarzynski Equality · Regime Classification · Physics-Informed Trading
Results · Quick Start · Paper · Citation
--- [](https://doi.org/10.5281/zenodo.19046564) > **First-ever empirical test of the Jarzynski equality on financial market data.** We map the perpetual futures funding rate mechanism to non-equilibrium statistical mechanics, validate on 6.2 years of Binance data (19,697 funding cycles), and derive physics-informed trading signals that significantly outperform naive funding arbitrage. **Author:** Ethan Lee Khoo Chuen · Independent Researcher · [ElvianElvyWork@gmail.com](mailto:ElvianElvyWork@gmail.com) --- ## The Idea in 60 Seconds Perpetual futures use a **funding rate** every 8 hours to anchor the contract price to spot. We discovered this mechanism is mathematically identical to a **driven particle in a harmonic potential** from statistical physics: | Market Quantity | Physics Analogue | Definition | |:---|:---|:---| | Percentage basis | Particle position | $(p_{\text{perp}} - p_{\text{spot}}) / p_{\text{spot}} \times 100\%$ | | Funding rate | External driving force | Applied every 8h | | Spot market | Thermal heat bath | Absorbs fluctuations | | Basis volatility | Temperature | $T = \kappa \cdot \text{Var}(b)$ | | Mean-reversion rate | Spring constant | $\kappa$ from AR(1) | | Entropy production | Irreversibility | $\sigma = W - \Delta F$ | This isn't a metaphor — the equations are exact. And the physics makes **testable predictions** about when funding arbitrage is safe vs. dangerous. --- ## Key Results ### 1. The Jarzynski Equality Holds for Bitcoin The JE ($\langle e^{-\beta\sigma}\rangle = 1$) holds to within **2% for BTC** and **3% for ETH** — the first empirical confirmation on financial data. | Asset | JE (raw) | JE (winsorized) | Deviation | |:---:|:---:|:---:|:---:| | **BTC** | 1.020 | 1.016 | 2.0% | | **ETH** | 1.032 | 1.020 | 3.2% | | **SOL** | overflow | 1.002 | 0.18% | ### 2. Relaxation Time Predicts JE Validity (Novel Finding) We discovered that the basis relaxation time $\tau = 1/\kappa$ determines whether the JE holds: | Asset | $\tau_{\text{relax}}$ | Funding Period | Ratio | JE Valid? | |:---:|:---:|:---:|:---:|:---:| | **BTC** | 7.6h | 8h | 0.96 | ✅ Yes | | **ETH** | 7.1h | 8h | 0.89 | ✅ Yes | | **SOL** | 12.3h | 8h | 1.53 | ❌ No | **When $\tau < 8$h:** basis equilibrates between cycles → JE holds → funding arb is safe. **When $\tau > 8$h:** basis persists → JE violated → market in non-equilibrium steady state. ### 3. Second Law of Thermodynamics | Asset | $\langle\sigma\rangle$ | $p$-value | Verdict | |:---:|:---:|:---:|:---:| | **BTC** | +0.135 | < 0.001 | **HOLDS** | | **ETH** | +0.035 | 0.016 | **HOLDS** | | **SOL** | −0.135 | 1.000 | **VIOLATED** | SOL's violation confirms it operates in a **non-equilibrium steady state** — exactly what the relaxation time analysis predicts. ### 4. Physics-Informed Trading Beats Naive Arbitrage Four thermodynamic signals → three-state regime classifier → dynamic position sizing: | Asset | V2 Physics Sharpe | Naive Sharpe | Improvement | $p$-value | |:---:|:---:|:---:|:---:|:---:| | **BTC** | **5.89** | 4.73 | +1.16 | < 0.001 | | **ETH** | **5.07** | 4.53 | +0.53 | 0.013 | | **SOL** | **0.73** | −0.25 | +0.98 | < 0.001 | **The SOL result is the star:** naive funding arb *loses* 4.2%. The physics-informed strategy *gains* 4.3% by correctly identifying and reducing exposure during NESS periods. > **Note:** High Sharpe ratios reflect the high-frequency nature of the strategy (1,095 settlements/year), not extraordinary alpha. Per-cycle Sharpe is ~0.18; the annualization factor $\sqrt{1095} \approx 33$ amplifies it. Absolute returns are 2–3% annualized. --- ## Quick Start ### Requirements - Python 3.11+ - [uv](https://docs.astral.sh/uv/) package manager (recommended) or pip ### Installation ```bash git clone https://github.com/ElvianElvy/fluctuation-theorem-perps.git cd fluctuation-theorem-perps uv pip install -e ".[dev]" ``` ### Run the Full Pipeline ```bash # Step 1: Synthetic validation (instant, no internet needed) python -m scripts.run_analysis # Step 2: Collect 6+ years of Binance data (~20 min, public API, no keys) python -m scripts.collect_data # Step 3: Full analysis — physics + strategy + figures python -m scripts.run_analysis ``` **Windows users:** Use Windows Terminal (not cmd.exe) for Unicode output. ### Output ``` output/ ├── figures/ # 43 publication-quality figures (PDF + PNG) │ ├── fig_synthetic_panel.png │ ├── fig7_relaxation.png │ ├── fig10_strategy_comparison_*.png │ └── ... └── results/ data/ └── ftp.duckdb # DuckDB database with all market data ``` --- ## Project Structure ``` fluctuation-theorem-perps/ │ ├── config/ │ └── settings.py # Pydantic configuration │ ├── data/ │ ├── collectors/ │ │ └── binance.py # Async Binance data collector │ └── storage/ │ └── db.py # DuckDB with ASOF JOIN │ ├── theory/ # Core physics │ ├── thermodynamic_quantities.py # E, W, ΔF, σ — all from market data │ ├── synthetic.py # Ornstein-Uhlenbeck simulator │ ├── market_temperature.py # β estimation from basis volatility │ ├── jarzynski.py # 3 JE estimators (numerically stable) │ ├── crooks.py # Detailed Fluctuation Theorem (KDE) │ └── entropy_production.py # Rolling σ(t), second law tests │ ├── strategy/ # Trading application │ ├── signals.py # 4 physics-derived signals │ ├── regime.py # 3-state thermodynamic classifier │ ├── backtest.py # V1 entropy-threshold backtester │ └── backtest_v2.py # V2 physics-informed (signed funding + basis risk) │ ├── analysis/ │ ├── validation.py # Full pipeline: synthetic → real → backtest │ ├── visualizations.py # 43 publication figures │ └── strategy_analysis.py # Strategy comparison + significance tests │ ├── scripts/ │ ├── collect_data.py # Data collection CLI │ └── run_analysis.py # Full pipeline runner │ ├── paper/ │ ├── main.tex # LaTeX source (18 pages) │ └── outline.md # Paper structure │ └── pyproject.toml # Dependencies and build config ``` --- ## Technical Details ### Data - **Source:** Binance public API (no authentication required) - **Assets:** BTCUSDT, ETHUSDT, SOLUSDT - **Period:** January 2020 – March 2026 (6.2 years) - **Volume:** 19,702 funding rates · 314,693 klines · 156,896 basis observations · 19,697 funding cycles - **Storage:** DuckDB columnar database with ASOF JOIN for time alignment ### Physics Framework - **Model:** Overdamped Langevin equation: $\dot{b} = -\kappa b - F + \xi$ - **Work protocol:** Sudden quench — $W = -F \cdot b_{\text{start}}$ - **Free energy:** $\Delta F = -F^2 / (2\kappa)$ - **Temperature:** $T = \kappa \cdot \text{Var}(b)$ from fluctuation-dissipation relation - **Validation:** Exact OU discretization with known analytics ($R^2 = 0.985$ on DFT) ### Trading Strategy - **Architecture:** Always-on delta-neutral with physics-based position sizing - **Regimes:** EQUILIBRIUM (100%) · WARM (60%) · NESS (25%) - **Fees:** 16 bps round-trip (maker/taker blend + 1 bps slippage) - **Protocol:** Walk-forward (360-cycle train, 90-cycle test, out-of-sample only) - **PnL model:** Signed funding + basis risk (no `abs()` — realistic) --- ## Four Novel Signals | # | Signal | Source | What it measures | |:---:|:---|:---|:---| | 1 | **Relaxation Ratio** | $r = 1/(8\kappa)$ | Basis mean-reversion speed vs funding period | | 2 | **Temperature Z-score** | $z = (\beta - \bar\beta)/\sigma_\beta$ | Market stability regime (cold = safe) | | 3 | **Entropy Rate** | $\dot\sigma = \beta(W - \Delta F)$ | Funding mechanism dissipation strength | | 4 | **JE Health** | $\|\langle e^{-\beta\sigma}\rangle - 1\|$ | How thermodynamic the market is | --- ## Paper The full paper (18 pages, 11 figures, 8 tables) is available in this repository: - **LaTeX source:** [`paper/main.tex`](paper/main.tex) - **Compiled PDF:** See releases --- ## Citation If you use this work in your research, please cite: ```bibtex @article{khoochuen2026fluctuation, title={Non-Equilibrium Thermodynamics of Cryptocurrency Perpetual Futures: Jarzynski Equality, Regime Classification, and Physics-Informed Trading}, author={Khoo Chuen, Ethan Lee}, year={2026}, note={Independent Research} } ``` --- ## License This project is licensed under the MIT License — see [LICENSE](LICENSE) for details. ---All trading results in this repository use virtual money only. No real capital was traded.