Homogeneous shear flow of a hard-sphere fluid: Analytic solutions

The analytical solutions for collision free trajectories in an N particle thermostatted hard-sphere system undergoing homogeneous shear were discussed. The solutions led to the equivalence of constant temperature and constant energy ensembles in the thermodynamic limit in equilibrium and the conditions for the nature of heat exchange with the environment in the system. The condition for appearance of the artificial string phase also followed from the solutions.