  Thermal waves are caused by pure diffusion: their amplitude is decreased by
more than a factor of 500 within a propagation distance of one wavelength. The
diffusion equation, which describes the temperature as a function of space and
time, is linear. For every linear equation the superposition principle is
valid, which is known as Huygens principle for optical or mechanical wave
fields. This limits the spatial resolution, like the Abbe diffraction limit in
optics. The resolution is the minimal size of a structure which can be detected
at a certain depth. If an embedded structure at a certain depth in a sample is
suddenly heated, e.g. by eddy current or absorbed light, an image of the
structure can be reconstructed from the measured temperature at the sample
surface. To get the resolution the image reconstruction can be considered as
the time reversal of the thermal wave. This inverse problem is ill-conditioned
and therefore regularization methods have to be used taking additional
assumptions like smoothness of the solutions into account. In the present work
for the first time methods of non-equilibrium statistical physics are used to
solve this inverse problem without the need of such additional assumptions and
without the necessity to choose a regularization parameter. For reconstructing
such an embedded structure by thermal waves the resolution turns out to be
proportional to the depth and inversely proportional to the natural logarithm
of the signal-to-noise ratio. This result could be derived from the diffusion
equation by using a delta-source at a certain depth and setting the entropy
production caused by thermal diffusion equal to the information loss. No
specific model about the stochastic process of the fluctuations and about the
distribution densities around the mean values was necessary to get this result.
