Demon in the details

The feature article by Eric Lutz and Sergio Ciliberto (Physics Today, September 2015, page 30 ) provides an interesting review of the basic theoretical ideas and recent experimental implementation of Maxwell’s demon and its relation to Rolf Landauer’s erasure principle. Unfortunately, the section on modern theory might give the impression that the second law of thermodynamics now has an extension that includes information and allows one to extract more work from a heat engine than the limit prescribed by the Carnot efficiency.

The problem is the formula for the work produced by the information-assisted heat engine, W = W_C + k_BT₁I, where W_C is the work that would be produced by a Carnot engine, T₁ is the temperature of the cold reservoir, and I is the amount of information the detector obtains about the state of the engine.

The process that leads to the “modern” work equation returns the heat engine, but not the system as a whole, to its initial state. To return the system to its initial state, as required by the very notion of the heat engine, one needs to erase the information obtained in the process of engine operation. Optimal erasure of that information will generate heat in the engine environment; that heat, in turn, will remove all the gains obtained by measurements and return the system efficiency to its Carnot value. The second law remains unchanged.