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Statistical mechanics of entropic forces: disassembling a toy

The notion of entropic forces often stays mysterious to students, especially to ones coming from outside physics. Although thermodynamics works perfectly in all cases when the notion of entropic force is used, no effort is typically made to explain the mechanical nature of the forces. In this paper we discuss the nature of entropic forces as conditional means of constraint forces in systems where interactions are taken into account as mechanical constraints and discuss several examples of such forces. We moreover demonstrate how these forces appear within the standard formalism of statistical thermodynamics and within the mechanical approach based on the Pope–Ching equation, making evident their connection with the equipartition of energy. The paper is aimed at undergraduate and graduate students studying statistical physics and the teachers teaching it.