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

Battle Count: 94

Highly relevant to quantitative trading, particularly in market microstructure, optimal execution, and algorithmic trading. The Financial Second Law provides rigorous no-arbitrage conditions for round-trip strategies. The fluctuation theorem offers a quantitative measure of market efficiency and bounds on profitable trading probability. The free energy framework connects individual execution costs to collective market behavior. The analytical examples (triangular, square-wave, ramp-up/decay strategies) directly inform execution algorithm design. The market temperature concept provides a novel calibration tool. However, the paper is primarily theoretical with only preliminary empirical validation, and practical implementation would require significant adaptation to real market conditions (latency, partial fills, non-stationarity).

The theoretical framework requires graduate-level knowledge of Itô calculus, convex analysis (Fenchel-Legendre transforms), large deviation theory, and statistical mechanics. The analytical results for prototypical strategies are tractable and well-derived. Empirical implementation requires high-frequency TAQ data processing, non-parametric impact estimation, convexity testing, and strategy clustering. The Gibbs measure calibration via MLE is straightforward. The multi-asset extension adds matrix operations. The quantum generalization and RL integration are speculative and highly complex. Overall, the core framework is implementable by a quantitative researcher with strong mathematical background, but full empirical validation is data-intensive.

The paper provides complete analytical derivations for all main results (Theorems 4.1, 5.1, Proposition 6.2), explicit calculations for three prototypical strategies (triangular, square-wave, ramp-up/decay), and empirical validation protocols. Code is available on GitHub (https://github.com/AIM-IT4/stochastic-thermo-finance). However, the empirical validation section (Section 8) only presents preliminary results on NASDAQ data (2015-2019) without full dataset access. The mathematical framework is self-contained and relies on graduate-level probability and convex analysis.