  Gibbs sampling is fundamental to a wide range of computer algorithms. Such
algorithms are set to be replaced by physics based processors$-$be it quantum
or stochastic annealing devices$-$which embed problem instances and evolve a
physical system into an ensemble to recover a probability distribution. At a
critical constraint to variable ratio, decision problems$-$such as
propositional satisfiability$-$appear to statistically exhibit an abrupt
transition in required computational resources. This so called, algorithmic or
computational phase transition signature, has yet-to-be observed in
contemporary physics based processors. We found that the computational phase
transition admits a signature in Gibbs' distributions and hence we predict and
prescribe the physical observation of this effect. We simulate such an
experiment, that when realized experimentally, we believe would represent a
milestone in the physical theory of computation.
