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A scenario for systems with slow dynamics is characterised by stating thatthere are several temperatures coexisting in the sample, with a singletemperature shared by all observables at each (widely separate) time-scale.  In preparation for the study of granular rheology, we show within thisframework that glassy systems with driving and friction that are generic and donot correspond to a thermal bath --- and whose microscopic `fast' motion ishence not thermal --- have a well-defined macroscopic temperature associated tothe slow degrees of freedom.  This temperature is what a thermometer coupled to the system will measure iftuned to respond to low frequencies, and since it can be related to the numberof stationary configurations, it is the formalisation of Edwards'`compactivity' ideas.Comment: Revised version: treatment of `tapping' deferre

journal of physics. condensed matter

Emergence of macroscopic temperatures in systems that are not thermodynamical microscopically: towards a thermodynamical description of slow granular rheology