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Time has been an elusive concept to grasp. Although we do not yet understand it properly, there have been advances made in regard to how we can explain it. One such advance is the Page–Wootters mechanism. In this mechanism, time is seen as an inaccessible coordinate and the apparent passage of time arises as a consequence of correlations between the subsystems of a global state. Here we propose a measure that captures the relational character of the mechanism, showing that the internal coherence is the necessary ingredient for the emergence of time in the Page–Wootters model. Also, we connect it to results in quantum thermodynamics, showing that it is directly related to the extractable work from quantum coherence.

The classical limit for generalized partition functions is obtained using coherent states. In this framework it is presented a general procedure to obtain all the corrections to the classical limit. In particular, the first and second order quantum corrections are worked out explicitly, and the classical limit for the Tsallis thermostatistics is determined. The results of this work generalize the ones obtained by E. Wigner (Phys. Rev. 40 (1932) 749) for usual statistical mechanics., latex, 12 pages, to appears in Phys. A