The equation of state of an ideal gas in two connected vessels

We consider a two-dimensional collisionless ideal gas in the two vessels. In one of them particles behavior is ergodic. Another one is known to be nonergodic. Significant part of the phase space of this vessel is occupied by islands of stability. It is shown, that gas pressure is uniform in the first vessel and highly uneven in second one. Distribution of particle residence times was considered. For nonergodic vessel it is found to be quite unusual: delta spikes on small times, then several sites of chopped sedate decay and finally exponential tail. Such unusual dependence is found to be connected with islands of stability, destroyed after vessels interconnection. Equation of gas state in the first vessel is obtained. It differs from the ordinary equation of ideal gas state by an amendment to the vessel’s volume. In this way vessel’s boundary affects the equation of gas state. Correlation of this amendment with a share of the phase space under remaining intact islands of stability is shown.