Hnizdo Vladimir, Gilson Michael K
Health Effects Laboratory Division, National Institute for Occupational Safety and Health, Morgantown, West Virginia 26505, USA.
Center for Advanced Research in Biotechnology, University of Maryland Biotechnology Institute, Rockville, Maryland 20850, USA.
Entropy (Basel). 2010 Mar 16;12(3):578-590. doi: 10.3390/e12030578.
The differential Shannon entropy of information theory can change under a change of variables (coordinates), but the thermodynamic entropy of a physical system must be invariant under such a change. This difference is puzzling, because the Shannon and Gibbs entropies have the same functional form. We show that a canonical change of variables can, indeed, alter the spatial component of the thermodynamic entropy just as it alters the differential Shannon entropy. However, there is also a momentum part of the entropy, which turns out to undergo an equal and opposite change when the coordinates are transformed, so that the total thermodynamic entropy remains invariant. We furthermore show how one may correctly write the change in total entropy for an isothermal physical process in any set of spatial coordinates.
信息论中的微分香农熵在变量（坐标）变化时会改变，但物理系统的热力学熵在这种变化下必须保持不变。这种差异令人困惑，因为香农熵和吉布斯熵具有相同的函数形式。我们表明，正则变量变换确实可以改变热力学熵的空间分量，就像它改变微分香农熵一样。然而，熵还有一个动量部分，当坐标变换时，它会发生大小相等、方向相反的变化，从而使总热力学熵保持不变。我们还展示了如何在任何一组空间坐标中正确写出等温物理过程的总熵变化。
