An Example of a Mechanical System whose Ensemble Average Energy, Starting with a Microcanonical Ensemble, Decreases after an Operation

Abstract

In this note we demonstrate the existence of a mechanical system that, beginning with a microcanonical ensemble, experiences a decrease in the expectation value of its energy as a result of a “return operation” (defined in the text). This finding leads us to a discussion in thermodynamics, from which we conclude that - provided that an assumption we make regarding our ability to select certain realizations of the system from an ensemble is valid - the existence of this system implies the violation of the Kelvin postulate. An examination of the specific system we study provides evidence suggesting that the type of system in which we are interested is quite rare.