98-212 CARATI A., GALGANI L.

On the specific heat of Fermi-Pasta-Ulam systems (410K, PostScript) Mar 20, 98

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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.

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