You seem to be missing the point. Ignoring for a second that the laws of thermodynamics themselves are based upon a handful of idealizations (the idealization of "thermal equilibrium", the idealization of "perfectly isolated system", the idealization of "perfect zero)...the laws of nature are encoded as formalisms/equations. Symbolic computations.

If you have no formalisms you can't compute any consequences - there is nothing to test. You have no science.

So treating Mathematics and science as "separate disciplines", even though they function as one symbiotic whole - that's the conceptual error.