Coarse-grained entropy balance of the Szilard engine

In order to reconcile the entropy reduction of a system through external interventions that are linked to a measurement with the second law of thermodynamics, there are two main proposals: (i) The entropy reduction is compensated by the entropy increase as a result of the measurement on the system (``Szilard principle"). (ii) The entropy reduction is compensated by the entropy increase as a result of the erasure of the measurement results (``Landauer/Bennett principle"). It seems that the LB principle is widely accepted in the scientific debate. In contrast, in this paper we argue for a modified S principle and criticize the LB principle with regard to various points. Our approach is based on the concept of ``conditional action", which is developed in detail. To illustrate our theses, we consider the entropy balance of a variant of the well-known Szilard engine, understood as a classical mechanical system.