A stroll among effective temperatures in aging systems: limits and perspectives

In this paper we present a short survey on the concept of effective temperature, on its onset as a glass former vitrifies, on the various definitions in literature and their limits of applicability. An exactly solvable model glass is employed to compare effective temperatures among them and to set a criterion for the occurrence of a universal extra temperature in the framework of a "two temperature thermodynamics" for off-equilibrium aging systems. It will be shown that aging in glass formers is not a sufficient requirement. As an instance, memory effects typical of glasses are not compatible with a unique effective temperature. Yet, a reduced range of applicability can still be established and investigated.