Quote from the Scotrail News feed-
Traditionally services on Boxing Day have been restricted to a very small number, mainly in the Strathclyde area.
But this year, trains will also run to and from Perth, Dunblane and Glenrothes, and between Bathgate and Edinburgh, giving more people the chance to travel to see family and friends at this special time of year.
The additions to the Boxing Day services include:
Bathgate to Edinburgh.
Glasgow to Alloa.
Edinburgh to Dunblane.
Edinburgh to Glenrothes via Dunfermline.
Edinburgh to Perth via Kirkcaldy.
Also note that Scottish Citylink are running many more services on 26 December and 2 January than in previous years, and also run from Edinburgh to Glasgow on Christmas Day, hourly, all day.