Entropic forces—making the connection between mechanics and thermodynamics in an exactly soluble model
Upper-level undergraduate texts in thermodynamics and statistical mechanics frequently describe a force as being of entropic origin if it represents the tendency of a system to evolve into a more probable state, rather than simply into one of lower potential energy. This concept is not easy to understand, as it arises in the context of systems in which no apparent force exists at zero temperature. It is only when thermal motion is introduced that an apparent driving force appears. This difficulty is compounded by the absence of any non-trivial soluble model. Here we provide insight into the nature of entropic forces by presenting an exactly soluble model in which the entropic force can be derived from both mechanical and thermodynamic analyses, with results that are shown to be identical.