Re: Duhamel principle and Lorentzians

On 12/26/2024 10:54 AM, Ross Finlayson wrote:

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.
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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.
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It seems this is a probable case in the differential
analysis, and there are at least some linked-looking
efforts, about Duhamel principle and implementing
gradient in Lorentzians, with a vanishingly small
amount of energy.
I think that the differential analysis needs more
integral analysis and the differintegro and the
integrodiffer, yet examples like this about Duhamel
are rather un-explored for sitting in the middle
of the Lorentzian.