Dynamical Temperature of a One-Dimensional Many-Body System inthe Lennard-Jones Model

A new way to derive the formula of the dynamical temperature by
using the invariance of the Liouville measure and the ergodicity
hypothesis is presented, based on the invariance of the functional under the transformation of the measure. The obtained dynamical temperature is intrinsic to the underlying dynamics of the system. A molecular dynamical simulation of a one-dimensional many-body system in the Lennard-Jones model has been performed. The temperature calculated from the Hamiltonian for the stationary state of the system coincides with that determined with the thermodynamical method.