Did Vardi write about this? I only found some other authors instead; is it possible you are referring to Yuri Manin instead? :
From https://arxiv.org/pdf/1010.2067
"Manin and Marcolli [20] derived similar results in a broader context and
studied phase transitions in those systems. Manin [18, 19] also outlined an
ambitious program to treat the infinite runtimes one finds in undecidable problems as singularities to be removed through the process of renormalization. In a manner reminiscent of hunting for the proper definition of the “one-element
field” F_un, he collected ideas from many different places and considered how
they all touch on this central theme. While he mentioned a runtime cutoff as
being analogous to an energy cutoff, the renormalizations he presented are uncomputable. In this paper, we take the log of the runtime as being analogous
to the energy; the randomness described by Chaitin and Tadaki then arises as
the infinite-temperature limit."
From https://arxiv.org/pdf/1010.2067 "Manin and Marcolli [20] derived similar results in a broader context and studied phase transitions in those systems. Manin [18, 19] also outlined an ambitious program to treat the infinite runtimes one finds in undecidable problems as singularities to be removed through the process of renormalization. In a manner reminiscent of hunting for the proper definition of the “one-element field” F_un, he collected ideas from many different places and considered how they all touch on this central theme. While he mentioned a runtime cutoff as being analogous to an energy cutoff, the renormalizations he presented are uncomputable. In this paper, we take the log of the runtime as being analogous to the energy; the randomness described by Chaitin and Tadaki then arises as the infinite-temperature limit."