= Local convex path action
{title2=$I(a)=\int_{-\infty}^0g(\dot a_s)ds$}
A local path action integrates a nonnegative convex cost g of the path's instantaneous input rate, assigning infinity to paths that are not absolutely continuous. When $g(\mu)=0$, the typical-rate path has zero cost. On any interval with prescribed total input, <Jensen inequality> makes a constant derivative minimize its cost. With a <queue workload> constraint this leads to <constant-rate burst paths> and the <linear workload rate for a local convex action>. Such a formula alone does not establish goodness in an unspecified path topology; goodness must be checked or assumed as part of the input large-deviation principle.
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