Phase transitions in periodically driven macroscopic systems.

We study the large-time behavior of a class of periodically driven macroscopic systems. We find, for a certain range of the parameters of either the system or the driving fields, the time-averaged asymptotic behavior effectively is that of certain other equilibrium systems. We then illustrate with a few examples how the conventional knowledge of the equilibrium systems can be made use of in choosing the driving fields to engineer new phases and to induce new phase transitions.