The resolution in photoacoustic imaging is limited by the acoustic bandwidth and therefore by acoustic attenuation, which can be substantial for high frequencies. This effect is usually ignored for photoacoustic reconstruction but has a strong influence on the resolution of small structures. The amount of information about the interior of samples, which can be gained in general by the detection of optical, thermal, or acoustical waves on the sample surface, is essentially influenced by the propagation from its excitation to the surface. Scattering, attenuation, and thermal diffusion cause an entropy production which results in a loss of information of propagating waves. Using a model based time reversal method, it was possible to partly compensate acoustic attenuation in photoacoustic imaging. To examine this loss of information in more detail, we have restricted us to "thermal waves" in one dimension, which can be realized experimentally by planar layers. Simulations using various boundary conditions and experimental results are compared. Reconstruction of the initial temperature profile from measurement data is performed by various regularization methods, the influence of the measurement noise (fluctuations) on the information loss during reconstruction is shown to be equal to the entropy production during wave propagation.