Information loss, entropy production and time reversal for dissipative and diffuse processes
Peter Burgholzer
备注：
28 pages; first part of this work has been accepted for publication (see P. Burgholzer, and G. Hendorfer: Limits of spatial resolution for thermography and other non-destructive imaging methods based on diffusion waves, International Journal of Thermophysics (2013)), but printing will take some time
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.
Time-reversal symmetries and equilibrium-like Langevin equations
格雷厄姆在Z. Physik B 26，397-405（1977），波动耗散关系可以被施加到一类非平衡马尔可夫朗之万方程上，该方程允许相应的福克-普朗克方程的定态解。由此产生的朗之万方程的平衡形式与非平衡哈密顿量相关联。在这里，我们提供了一些明确的见解，这个哈密顿可能会失去其时间反演不变性和如何“反应”和“耗散”通量失去其独特的时间反演对称性。力和通量之间的反对称耦合矩阵不再源自泊松括号，并且在稳态下，“反应性”通量有助于（“管家”）熵产生。非平衡哈密顿量的时间反演的偶数和奇数部分对熵的贡献在性质上不同，但在物理上有指导意义。我们发现的情况下，由于噪声波动是唯一负责的耗散。最后，这种结构产生了一个新的，物理上相关的frenesy实例。
