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Maxwell's relations as Hamilton's equations: a symplectic and variational framework
We develop a geometric framework in which classical thermodynamics is reformulated as a Hamiltonian dynamical system. An explicit canonical mapping $(q,p,t,H)\leftrightarrow(V,-P,S,-T)$ identifies Maxwell's relations as the characteristic equations of the thermodynamic Poincaré--Cartan one-form, in
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