Price Impact, Round-Trip Trading, and a Thermodynamic No-Arbitrage Bound

Summary

This paper uses ideas from stochastic thermodynamics to model price impact and examine round-trip trading strategies. It treats a trading cycle as a non-equilibrium process, interprets impact as dissipated work, and treats market noise as thermal fluctuation. Under general convex impact functionals, it derives a constraint that round-trip strategies cannot have positive expected profit, and a fluctuation theorem bounding the probability of a profitable cycle in terms of dissipated work and market volatility.

The framework also defines a Gibbs-weighted ensemble of strategies and decomposes free energy into expected cost, strategy entropy, and a market temperature parameter. Analytical results for representative strategies and proposed empirical validation protocols are described, but the provided text gives no empirical findings. The conclusions are theoretical and depend on the stated impact assumptions; the summary does not specify the protocol's data requirements or how well the inequalities hold in observed markets.

Key ideas

• The framework models price impact as dissipative work within a trading cycle.
• For convex impact functionals, expected profit from a round trip is non-positive.
• A fluctuation theorem relates profitable-cycle probability to dissipated work and market volatility.
• A Gibbs measure over strategies connects expected cost, strategy entropy, and a market temperature parameter.
• The paper proposes empirical tests but reports no validation results in the provided description.

Tags

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


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









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.

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