Information loss, entropy production and time reversal for dissipative and diffuse processes

Abstract

In non-destructive imaging the information about the spatial pattern of a samples interior has to be transferred to the sample surface by certain waves, e.g. ultrasound or electromagnetic waves. At the sample surface these waves can be detected and the interior structure is reconstructed from the measured signals. The amount of information about the interior of the sample, which can be gained from the detected waves on the sample surface, is essentially influenced by the propagation from its excitation to the surface. Scattering, dissipation, or diffusion causes entropy production and a loss of information for the propagating waves, and therefore results in a loss of resolution for imaging the interior structure. There have been made several attempts to compensate these diffusive or dissipative effects to get a higher resolution for the reconstructed images of the samples interior. In this work it is shown that thermodynamical fluctuations limit this compensation and therefore also the spatial resolution for non-destructive imaging at a certain depth is limited. We describe one example for diffusion and another one for dissipation and the loss of information is modeled by stochastic processes. For both examples the thermodynamic entropy production is equal to the loss of information, which results in a theoretical limit for the achievable spatial resolution in the reconstructed image.