The gas model and its phase

The gas model and its phase. Let us take a gas model consisting of N identical polyatomic molecules, each having r degrees of freedom.61 Let us define the phase (of motion) of the gas model at time t as the set of the following 2rN data which determine exactly the simultaneous configuration and motion of the N molecules  

The atomic motions change the configurations of the atoms (g f , gf), while the external forces, the forces between the atoms of the same molecule and the forces which act in every collision, change the velocities (and therefore also the momenta p, , p ). The corresponding changes in the phase of the gas model are expressed by the Hamiltonian equations of motion 69 

Unless explicitly stated to the contrary, we will assume in the following considerations that the external forces do not change with time.70 

In this case E depends only on the g s and p s, but does not explicitly depend on t. The same holds for the quantities 

It is well known that the 2rN integrals of the equations of (22) can be expressed in the following form 71 

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