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

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  • 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.

Suggested Citation

  • Amit Kumar Jha, 2025. "A Stochastic Thermodynamics Approach to Price Impact and Round-Trip Arbitrage: Theory and Empirical Implications," Papers 2512.03123, arXiv.org.
    • Handle: RePEc:arx:papers:2512.03123
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