There are many different specific definitions of energy within different physics fields: In thermodynamics we have at least U (system internal energy), F (Helmholtz Free Energy), G (Gibbs Free Energy), H (Enthalpy). Or we have the relativistic stress-energy-momentum tensor, etc.
Various forms or configurations of energy seem to be included/excluded in these different definitions.
I'm looking for the most appropriate "type" of energy to use in quantifying the potential to disrupt (disorder) an ordered system. That is, some amount of "available" energy that can cause increase of entropy of the system. I do not want to get more specific than what I've said about what kind of ordered system it is. Just a configuration of matter and energy that has less than that amount of matter/energy's maximum possible entropy so has the potential to be disordered.
Disordering energy/matter-with-energy could come from outside the system I suppose, or be energy/mass within the system. So I guess we're talking about a thermodynamically open system, but thermodynamics tends to scope out energy that's locked up in/as the mass of matter.
For the most general case of describing energy available to disorder any ordered system, what type of energy definition should I use and why?