Hamiltonian and Lagrangian formalisms of mutations in cluster algebras   and application to dilogarithm identities
  We introduce and study a Hamiltonian formalism of mutations in cluster algebras using canonical variables, where the Hamiltonian is given by the Euler dilogarithm. The corresponding Lagrangian, restricted to a certain subspace of the phase space, coincides with the Rogers dilogarithm. As an application, we show how the dilogarithm identity associated with a period of mutations in a cluster algebra arises from the Hamiltonian/Lagrangian point of view. 
Michael Gekhtman, Tomoki Nakanishi, Dylan Rupel
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