🤖 AI Summary
This paper addresses price impact modeling and the feasibility of round-trip arbitrage in financial markets. Methodologically, it pioneers the application of stochastic thermodynamics to finance: trading cycles are formalized as nonequilibrium thermodynamic processes, price impact is identified with dissipated work, and market noise is mapped onto thermal fluctuations. Building on this analogy, the authors formulate a “Financial Second Law,” proving that under convex price impact, the expected profit of any round-trip trading strategy is nonpositive. Leveraging tools from convex analysis, Gibbs measures, and statistical ensembles, they establish a bridge between macroscopic market constraints and microscopic trade structures, deriving testable no-arbitrage inequalities and closed-form solutions for canonical strategies. The results uncover the physical underpinnings of market efficiency and provide a unified theoretical foundation—and empirically verifiable pathway—for no-arbitrage conditions.
📝 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.