Peter Shor commented on this post:
years of experience in theoretical computer science says that the thermodynamic behavior of two NP complete problems are in general not similar.
What do we know about the distribution/thermodynamics of $A$ w.r.t to $B$ if we know that $A \le_M B$ (there is a reduction from $B$ to $A$) or where we know that $A,B \in C$ where $C$ is some complexity class ($P$, $NP$, co-$NP$, etc.). I guess it's hard/impossible/wrong to use complexity theory which takes mostly the worst case and refer about thermodynamics, has a work to study thermodynamics of problems been done before?
What can we say on the thermodynamics if there isn't a reduction from $A$ to $B$, or given their complexity classes?