Duhamel principle and Lorentzians

Looking into Duhamel principle, with the idea that it's
like a heat equation where heat's generated at time t position x,
notice that it makes for the Laplacian and that its extra
term t - tau is just like the Lorentzian's -t when d^2.
So, Duhamel's principle sort of advises that it's a usual
kind of concern, then to model the least-action/least-gradient
of time-irreversibility and entropy, you'll notice, having
the same sort of idea, and the ability to re-write what's
about the statistical ensemble the thermo second law,
in terms of extracting out what's Duhamel principle,
to Lorentzians.