A Demon of Efficiency The Second Law: In Physics and in Finance

Twentieth-century physics is noted for its plethora of " thought experiments " , mostly provoked by the counterintuitive nature of quantum phenomena. One need only consider the famous Schrödinger's Cat Experiment or the Einstein-Podolsky-Rosen (EPR) Paradox, which address the question of the properties of a quantum object in its unobserved state. These types of experiments, which cannot generally be actually performed in a laboratory setting, have greatly sharpened our understanding of physical phenomena, as well as served as jumping-off points for a bewildering array of philosophical speculation and argumentation about the " true " nature of the physical world. But it did not take the appearance of quantum theory to give rise to such gedanken experiments. The notion was already well-entrenched even in classical physics of the nineteenth century. And certainly the most famous such thought experiment was put forth by the greatest physicist of the time, James Clerk Maxwell, in order to focus on epistemologi-cal puzzles arising in thermodynamics. The question that concerned Maxwell was whether there was some way around the (in)famous Second Law of Thermodynamics, which states that every closed physical system moves to a state of maximal disorder (entropy). In short, if left to themselves physical systems prefer a " messy " rather than structured equilibrium state. To illustrate the problem, Maxwell invented his famous " demon " , an imaginary being who was placed into a container of molecules that were isolated from the physical environment. For the sake of simplcity, assume there are just two types of molecules, " fast " ones and " slow " ones, or to use colors, White and Black ones. Initially, the molecules are more