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We introduce a new concept of finite-time entropy which is a local version ofthe classical concept of metric entropy. Based on that, a finite-time versionof Pesin's entropy formula and also an explicit formula of finite-time entropyfor $2$-D systems are derived. We also discuss about how to apply thefinite-time entropy field to detect special dynamical structures such asLagrangian coherent structures.

A new concept of local metric entropy for finite-time nonautonomous dynamical systems