Information thermodynamics of financial markets: the Glosten-Milgrom model

The Glosten-Milgrom model describes a single asset market, where informed traders interact with a market maker, in the presence of noise traders. We derive an analogy between this financial model and a Szil\'ard information engine by {\em i)} showing that the optimal work extraction protocol in the latter coincides with the pricing strategy of the market maker in the former and {\em ii)} defining a market analogue of the physical temperature from the analysis of the distribution of market orders. Then we show that the expected gain of informed traders is bounded above by the product of this market temperature with the amount of information that informed traders have, in exact analogy with the corresponding formula for the maximal expected amount of work that can be extracted from a cycle of the information engine. This suggests that recent ideas from information thermodynamics may shed light on financial markets, and lead to generalised inequalities, in the spirit of the extended second law of thermodynamics

Phase compositions and equilibria in the CaO-Al2O3-Fe2O3-SO3 system, for assemblages containing ye'elimite and ferrite Ca-2(Al,Fe)O-5

Phase equilibria in the CaO-Al2O3-Fe2O3-SO3 system have been studied, mainly at 1325 degrees C. In particular the solid solution compositions of ye'elimite Ca-4(Al6O12)SO4 and brownmillerite (C-2(A,F)) phases have been analysed and used to estimate the composition boundaries of these phases in their co-existence with liquid at 1325 degrees C. Sulfate and iron oxide facilitate the formation of a liquid phase, whose amount increases with overall Fe2O3 content. However, the solubility of sulfate in this liquid phase is very low and liquid formation tends to lead to the volatilisation of sulfate in unsealed samples. (C) 2013 Elsevier Ltd. All rights reserved