How FAH works: Thermodynamic alchemy

One of the remarkable strengths of thermodynamics is that it is in many ways more general than many of the laws of physics.  One of the key concepts in thermodynamics is that of a state function.  The key aspect of a state function is that if you’re interested in the differences in a state function between some initial and final state, it doesn’t matter what you do to get from the initial to the final — whatever path you take would get you the same value for the difference of the state function.

How is this useful?  Well, often we can take paths in simulations which are not possible in reality, but since the values of state functions only depend on the initial and final state, as long as those as the same as in reality, we get the same result!  One key way we use to take advantage of this is thermodynamic alchemy.  For example, often one is interested in the difference between an amino acid could be a single methyl group.  In simulation, we can turn a proton alchemically into a methyl group and calculate everything we need thermodynamically, even if this isn’t possible to do experimentally in a direct way!