Recent studies have shown that secular evolution of triple systems can play a major role in the evolution and interaction of their inner binaries. Very few studies explored the stellar evolution of triple systems, and in particular the mass-loss phase of the evolving stellar components. Here we study the dynamical secular evolution of hierarchical triple systems undergoing mass loss. We use the secular evolution equations and include the effects of mass loss and mass transfer, as well as general relativistic effects. We present various evolutionary channels taking place in such evolving triples, and discuss both the effects of mass loss and mass transfer in the inner binary system, as well as the effects of mass loss/transfer from an outer third companion. We discuss several distinct types/regimes of triple secular evolution, where the specific behavior of a triple system can sensitively depend on its hierarchy and the relative importance of classical and general relativistic effects. We show that the orbital changes due to mass-loss and/or mass-transfer processes can effectively transfer a triple system from one dynamical regime to another. In particular, mass loss/transfer can both induce and quench high-amplitude (Lidov-Kozai) variations in the eccentricity and inclination of the inner binaries of evolving triples. They can also change the system dynamics from an orderly periodic behavior to a chaotic one, and vice versa.
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