1 research outputs found
Entropy: From Black Holes to Ordinary Systems
Several results of black holes thermodynamics can be considered as firmly
founded and formulated in a very general manner. From this starting point we
analyse in which way these results may give us the opportunity to gain a better
understanding in the thermodynamics of ordinary systems for which a
pre-relativistic description is sufficient. First, we investigated the
possibility to introduce an alternative definition of the entropy basically
related to a local definition of the order in a spacetime model rather than a
counting of microstates. We show that such an alternative approach exists and
leads to the traditional results provided an equilibrium condition is assumed.
This condition introduces a relation between a time interval and the reverse of
the temperature. We show that such a relation extensively used in the black
hole theory, mainly as a mathematical trick, has a very general and physical
meaning here; in particular its derivation is not related to the existence of a
canonical density matrix. Our dynamical approach of thermodynamic equilibrium
allows us to establish a relation between action and entropy and we show that
an identical relation exists in the case of black holes. The derivation of such
a relation seems impossible in the Gibbs ensemble approach of statistical
thermodynamics. From these results we suggest that the definition of entropy in
terms of order in spacetime should be more general that the Boltzmann one based
on a counting of microstates. Finally we point out that these results are
obtained by reversing the traditional route going from the Schr\"{o}dinger
equation to statistical thermodynamics