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

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

Jian Gao
Lufeng Zhang
Ping Fang
Pu Ke
Jin Wu
Yue Liu
Haijun Zhou
Published on 4/16/2026
Equities
Crypto
Stocks
Momentum
Reversal
Market timing
Risk management

This paper introduces a fluctuation-theorem-like diagnostic for financial markets by comparing holding-time distributions of long and short trading positions generated from the same price history using symmetric take-profit and stop-loss rules. The log-ratio of the two distributions, Φ(dp), exhibits a robust crossover: it remains nearly constant at short durations and becomes approximately linear at longer durations, implying an exponential directional asymmetry. This structure is observed across equity indices, individual stocks, and cryptocurrencies. The tail slope defines an effective market temperature, Tm = 1/|k|, which serves as a coarse-grained measure of fluctuation intensity and reveals temporal patterns not visible in price series alone, including a global minimum around the enactment of the One Big Beautiful Bill Act in July 2025.

The authors identify the minimal stochastic mechanism using a Bachelier diffusion benchmark. While independent first-passage statistics produce exponential tails in holding-time distributions, they yield a saturating Φ(dp) because long and short positions share the same leading decay rate. In contrast, when positions are opened sequentially along a single price trajectory, pathwise correlations between overlapping trades generate direction-dependent subleading relaxation spectra in a coarse-grained Markov description. This converts correlations into a linear tail in Φ(dp), reproducing the empirical asymmetry. The mechanism is thus a finite-time, pre-asymptotic effect of coarse graining, analogous to hidden entropy production in stochastic thermodynamics. The work establishes a symmetry-based diagnostic of irreversibility in financial markets and demonstrates its utility for detecting regime shifts and system-wide correlations.

Highlights

  • 1Introduces a fluctuation-theorem-like diagnostic for directional asymmetry in financial markets using symmetric long/short trading rules.
  • 2Discovers a robust crossover in the log-ratio of holding-time distributions: constant at short durations and linear at long durations, implying exponential asymmetry.
  • 3Defines an effective market temperature from the tail slope, capturing fluctuation intensity and revealing temporal structure not visible in price series.
  • 4Shows that the asymmetry arises from pathwise correlations in sequential trading, not from microscopic symmetry breaking, and is reproduced by a correlated Bachelier model.
  • 5Provides a Markov-chain mechanism where direction-dependent subleading relaxation spectra generate the observed asymmetry as a finite-time effect.

Methods

  • M
    Coarse-grained holding-time analysis: construct long and short trading ensembles from the same price history using symmetric take-profit/stop-loss thresholds.
  • M
    Bachelier first-passage benchmark: simulate arithmetic Brownian motion with absorbing boundaries to compare uncorrelated and correlated ensemble constructions.
  • M
    Markov-chain modeling: represent the sequence of first-passage times as a Markov chain on discretized duration states, analyzing stationary distributions and subleading eigenvalues.
  • M
    Sliding-window estimation: compute effective market temperature over time to study temporal variation and correlation with major events.

Results

  • R
    The symmetry diagnostic Φ(dp) shows a short-duration plateau near zero and an approximately linear tail at longer durations across equity indices, stocks, and cryptocurrencies.
  • R
    The effective market temperature Tm = 1/|k| exhibits pronounced temporal variation, with deep minima coinciding with the enactment of the One Big Beautiful Bill Act in July 2025.
  • R
    The uncorrelated Bachelier model yields exponential tails in holding-time distributions but a saturating Φ(dp), while the correlated version reproduces the linear tail.
  • R
    Markov-chain analysis reveals that the asymptotic decay rate is direction-independent, but subleading eigenvalues differ between long and short directions, generating the asymmetry at finite times.
  • R
    The asymmetry is a coarse-graining effect: pathwise correlations from overlapping positions induce direction-dependent relaxation spectra, not a violation of microscopic buyer-seller pairing.
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