Statistical mechanics of quartic oscillators

Abstract

We study statistical mechanics of quartic oscillator with two degrees of freedom, which is known to be chaotic almost everywhere except in a few regions of the parameter range. We obtain exact expressions for temperature, entropy, and distribution functions. Temperature is also obtained numerically by time averaging the kinetic energy and using equipartition theorem and agrees with our expressions when the system is almost chaotic. We further generalize our model to quartic oscillators with N degrees of freedom, and exact expressions for thermodynamic quantities are obtained. As N→∞, standard statistical mechanics results are recovered. We also discuss pressure, density, and equation of state of this system.