Classical specific heat of an atomic lattice at low temperature, revisited

We present results of a standard (constant energy) molecular dynamics simulation of a Lennard-Jones lattice at low temperature. The kinetic energy fluctuations exhibit an anomalous behavior, due to a dynamics which is only weakly chaotic. Such a dynamics does not allow the use of the usual microcanonical equilibrium formula to compute the specific heat. We devise a different method for computing the specific heat, which exploits just the weak chaos at low temperature. The result is that at low temperature this “revisited” specific heat is lower than the classical value, and approaches zero when the temperature goes to zero. Only for exceedingly long trajectories does the specific heat approach the classical value, with the exception of the very low temperature range. These results prompt a reconsideration, in the frame of modern nonlinear dynamics, of early intuitions by Nernst and Jeans.