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.

中文翻译：

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主动热成像中空间分辨率的热力学极限

热波是由纯扩散引起的：在一个波长的传播距离内​​，它们的振幅减少了 500 多倍。将温度描述为空间和时间的函数的扩散方程是线性的。对于每一个线性方程，叠加原理都是有效的，这就是光或机械波场的惠更斯原理。这限制了空间分辨率，就像光学中的阿贝衍射极限一样。分辨率是可以在特定深度检测到的结构的最小尺寸。如果样品中某个深度处的嵌入结构突然被加热，例如通过涡流或吸收光，则可以从样品表面测得的温度重建该结构的图像。为了获得分辨率，可以将图像重建视为热波的时间反转。这个逆问题是病态的，因此必须使用正则化方法，同时考虑解决方案的平滑性等额外假设。在目前的工作中，首次使用非平衡统计物理学的方法来解决这个逆问题，而无需这些额外的假设，也无需选择正则化参数。对于通过热波重建这种嵌入结构，分辨率与深度成正比，与信噪比的自然对数成反比。这个结果可以从扩散方程中通过使用一定深度的 delta 源并将热扩散引起的熵产生设置为等于信息损失来推导出来。不需要关于波动的随机过程和关于平均值周围分布密度的特定模型来获得这个结果。