CARATI A., GALGANI L.
On the specific heat of Fermi-Pasta-Ulam systems
(410K, PostScript)

ABSTRACT.  The specific heat of Fermi Pasta Ulam systems was  up to now estimated
through the energy fluctuations of  a suitable subsystem, and opposite
answers were apparently provided concerning its possible vanishing for
vanishing temperatures. 
 In the present paper a more ``realistic'' numerical implementation of
the specific  heat   measurement  is   discussed,  which   mimics  the
interaction of the  FPU system  with  a calorimeter. This is  obtained
through a model   inspired by  one already  discussed   by Kelvin  and
Poincar\'e  in  connection   with   the  foundations   of  statistical
thermodynamics.  It is found that there exists a ``freezing'' critical
temperature below which  the relaxation times for  equilibrium between
FPU system and calorimeter become relevant, so that the system 
  presents aging and    hysteresis  features very    similar to  those
familiar in spin glasses theory.  In particular,  in the frame of such
a point of  view  involving finite long  times,  the specific  heat is
found to vanish for vanishing temperatures.