Fuentes Jesús, Gonçalves Jorge
Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Esch-sur-Alzette, L-4367 Luxembourg, Luxembourg.
Department of Plant Sciences, Cambridge University, Cambridge CB2 3EA, UK.
Entropy (Basel). 2022 Aug 5;24(8):1080. doi: 10.3390/e24081080.
Rényi entropy was originally introduced in the field of information theory as a parametric relaxation of Shannon (in physics, Boltzmann-Gibbs) entropy. This has also fuelled different attempts to generalise statistical mechanics, although mostly skipping the physical arguments behind this entropy and instead tending to introduce it artificially. However, as we will show, modifications to the theory of statistical mechanics are needless to see how Rényi entropy automatically arises as the average rate of change of free energy over an ensemble at different temperatures. Moreover, this notion is extended by considering distributions for isospectral, non-isothermal processes, resulting in relative versions of free energy, in which the Kullback-Leibler divergence or the relative version of Rényi entropy appear within the structure of the corrections to free energy. These generalisations of free energy recover the ordinary thermodynamic potential whenever isothermal processes are considered.
雷尼熵最初是在信息论领域作为香农（在物理学中为玻尔兹曼 - 吉布斯）熵的参数化松弛而引入的。这也激发了对统计力学进行推广的不同尝试，尽管大多跳过了该熵背后的物理依据，而是倾向于人为引入它。然而，正如我们将展示的，无需对统计力学理论进行修改就能明白雷尼熵如何作为不同温度下系综中自由能的平均变化率自动出现。此外，通过考虑等谱、非等温过程的分布来扩展这一概念，从而产生自由能的相对版本，其中库尔贝克 - 莱布勒散度或雷尼熵的相对版本出现在自由能修正结构中。只要考虑等温过程，这些自由能的推广就能恢复普通的热力学势。
