You should be able program the fan to come on for up to four periods per day. This feature is off by default. You will need to go into the service menu to turn on the programmable fan feature.

Below is a link to the installation manual. You can enter the service manual by holding down the advanced button for 10 seconds. Go into the setup menu and select thermostat submenu. You should find the programmable fan setting. Turn it on if it is set to off. Exit the service menu. You should then push the schdule button and the push the fan button on the upper right. A scheduling menu should appear for the fan operation.

Here is a link that might be useful: Bryant Evolution installation manual

Unfortunately it does not, since I wanted the identical Carrier model to randomly cirucate to even out temps in my two level home. I instead have the fan continuously on low for two of the four periods as mike_home suggested. With the variable speed motor in the Evolution/Infinity models that is a quiet and energy efficient compromise.

I recently noticed there are separate fan terminals on the main furnace board that can be separately wired up to provide fan control. I think another cheap thermostat with recirculating control or an Air Cycler could be wired here for random fan circulation, without losing benefit of the Evolution stat.

Any issues with running the fan on low for long periods of time? I'd want the fan to circulate at least for the sleep period, and maybe the evening period as well.

Running the fan on low is not a problem. In the summer it may cause the humidity to rise. This should not be a problem for the Evolution system since it will cool to dehumify as needed.

Try it and see if you like to results. You can always turn it off.