A Irreversible processes. Heat equation, diffusion equation

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Both the heat equation and the diffusion equation describe processes which are irreversible, because the equations have an odd time derivative. But how can these equations describe the real world when we know that all processes in nature are reversible, information is always conserved? But these equations seems to describe processes in which information is not conserved.
 
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Who says all processes in nature are reversible?
Because microscopically all processes have a time reversal symmetry.
 

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