A Stochastic Thermodynamics Approach to Price Impact and Round-Trip Arbitrage: Theory and Empirical Implications

ArXiv ID: 2512.03123 “View on arXiv”

Authors: Amit Kumar Jha

Abstract

This paper develops a comprehensive theoretical framework that imports concepts from stochastic thermodynamics to model price impact and characterize the feasibility of round-trip arbitrage in financial markets. A trading cycle is treated as a non-equilibrium thermodynamic process, where price impact represents dissipative work and market noise plays the role of thermal fluctuations. The paper proves a Financial Second Law: under general convex impact functionals, any round-trip trading strategy yields non-positive expected profit. This structural constraint is complemented by a fluctuation theorem that bounds the probability of profitable cycles in terms of dissipated work and market volatility. The framework introduces a statistical ensemble of trading strategies governed by a Gibbs measure, leading to a free energy decomposition that connects expected cost, strategy entropy, and a market temperature parameter. The framework provides rigorous, testable inequalities linking microstructural impact to macroscopic no-arbitrage conditions, offering a novel physics-inspired perspective on market efficiency. The paper derives explicit analytical results for prototypical trading strategies and discusses empirical validation protocols.

Keywords: price impact, stochastic thermodynamics, Financial Second Law, fluctuation theorem, Gibbs measure, General Equities/Market Microstructure

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper employs advanced mathematical concepts from stochastic thermodynamics, including Itô calculus, convex analysis, large deviation theory, and rigorous proofs of structural theorems, leading to a high math complexity score. However, it presents only theoretical frameworks and analytical derivations with no data, code, backtests, or implementation details for empirical validation, resulting in low empirical rigor.

  flowchart TD
    A["Research Goal: Model Price Impact & Arbitrage<br>via Stochastic Thermodynamics"] --> B["Key Methodology<br>Thermodynamic Trading Cycle Framework"]

    subgraph B ["Methodology"]
        direction TB
        M1["Import Stochastic Thermodynamics<br>to Financial Processes"]
        M2["Treat Price Impact as Dissipative Work<br>& Market Noise as Thermal Fluctuations"]
        M3["Define Gibbs Measure for<br>Trading Strategy Ensemble"]
    end

    B --> C["Computational Processes & Data<br>Derivation of Theoretical Bounds"]

    subgraph C ["Computational Processes"]
        direction TB
        P1["Derive Financial Second Law<br>Convex Impact → Non-Positive Expected Profit"]
        P2["Apply Fluctuation Theorem<br>Bound P(Profitable Cycle) vs Dissipation"]
        P3["Perform Free Energy Decomposition<br>Connect Cost, Entropy, & Market Temp"]
    end

    C --> D["Key Findings & Outcomes"]

    subgraph D ["Outcomes"]
        direction TB
        F1["Structural No-Arbitrage Constraint"]
        F2["Testable Microstructural Inequalities"]
        F3["Physics-Inspired Market Efficiency View"]
    end