A Statistical Mechanical View of Kalman Filtering

We develop a physical analogy for the Kalman-Bucy filter, in which the partially observed signal describes a statistical mechanical system interacting with a heat bath. The ‘universe’ comprising this system and the heat bath obeys a non-decrease law of entropy similar to the Second Law of Thermodynamics. However, this law can be violated in the presence of partial observations. Like Maxwell’s demon, the filter uses observations to extract work from the signal, thus ‘cooling’ it, but without causing any increase in entropy. The analogy provides a quantitative example of Landauer’s Principle. Further analogies and generalisations are briefly mentioned.