Maxwell’s Demon and Information Theory in Market Efficiency: A Brillouin’s Perspective

Abstract

By using Brillouin’s perspective on Maxwell’s demon, we determine a new way to describe investor behaviors in financial markets. The efficient market hypothesis (EMH) in its strong form states that all information in the market, public or private, is accounted for in the stock price. By simulations in an agent-based model, we show that an informed investor using alternative data, correlated to the time series of prices of a financial asset, is able to act as a Maxwell’s demon on financial markets. They are then able to perform statistical arbitrage consistently with the adaptive market hypothesis (AMH). A new statistical test of market efficiency provides some insight into the impact of the demon on the market. This test determines the amount of information contained in the series, using quantities which are widespread in information theory such as Shannon’s entropy. As in Brillouin’s perspective, we observe a cycle: Negentropy->Information->Negentropy. This cycle proves the implication of the investor depicted as a Maxwell’s demon in the market with the knowledge of alternative data.