Concept

# Entropic force

Summary
In physics, an entropic force acting in a system is an emergent phenomenon resulting from the entire system's statistical tendency to increase its entropy, rather than from a particular underlying force on the atomic scale. Mathematical formulation In the canonical ensemble, the entropic force \mathbf F associated to a macrostate partition {\mathbf{X}} is given by : \mathbf{F}(\mathbf{X}0) = T \nabla\mathbf{X} S(\mathbf{X})|_{\mathbf{X}_0}, where T is the temperature, S(\mathbf{X}) is the entropy associated to the macrostate \mathbf{X}, and \mathbf{X}_0 is the present macrostate. Examples Pressure of an ideal gas The internal energy of an ideal gas depends only on its temperature, and not on the volume of its containing box, so it is not an energy effect that tends to increase the volume of the box as gas pressure does. This
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