Measuring Thermodynamic Stability
Thermodynamics isn't quite that general.  It will tell you about the possibility of going from one well-defined state to another well-defined state, but as has been said, there is no way to do it in general.  What you are asking is akin to "is it hard to get there from here?" without specifying where both here and there are.

So you need to specify enough variables such as temperature or composition to unambiguously determine both the initial and final states.  How many variables do you need?  The Gibbs phase rule provides the answer.  Once that has been done, your question can be answered.