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

TL;DR

This paper applies stochastic thermodynamics to model financial market impact and arbitrage, establishing fundamental constraints and testable inequalities that connect microstructure effects to market efficiency.

Contribution

It introduces a physics-inspired framework that models trading as a thermodynamic process, deriving new laws and bounds for arbitrage and impact in financial markets.

Findings

Proves a Financial Second Law limiting arbitrage profits.

Derives fluctuation theorems bounding profitable cycle probabilities.

Provides analytical results for specific trading strategies.

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.