Fagerholm Erik D, Dezhina Zalina, Moran Rosalyn J, Turkheimer Federico E, Leech Robert
Department of Neuroimaging, King's College London, United Kingdom.
Department of Neuroimaging, King's College London, United Kingdom.
Neurosci Biobehav Rev. 2023 Mar;146:105070. doi: 10.1016/j.neubiorev.2023.105070. Epub 2023 Feb 1.
Entropy is not just a property of a system - it is a property of a system and an observer. Specifically, entropy is a measure of the amount of hidden information in a system that arises due to an observer's limitations. Here we provide an account of entropy from first principles in statistical mechanics with the aid of toy models of neural systems. Specifically, we describe the distinction between micro and macrostates in the context of simplified binary-state neurons and the characteristics of entropy required to capture an associated measure of hidden information. We discuss the origin of the mathematical form of entropy via the indistinguishable re-arrangements of discrete-state neurons and show the way in which the arguments are extended into a phase space description for continuous large-scale neural systems. Finally, we show the ways in which limitations in neuroimaging resolution, as represented by coarse graining operations in phase space, lead to an increase in entropy in time as per the second law of thermodynamics. It is our hope that this primer will support the increasing number of studies that use entropy as a way of characterising neuroimaging timeseries and of making inferences about brain states.
熵不仅仅是系统的一种属性——它是系统和观察者的一种属性。具体而言，熵是对由于观察者的局限性而在系统中产生的隐藏信息量的一种度量。在这里，我们借助神经系统的简化模型从统计力学的第一原理出发阐述熵。具体来说，我们在简化的二态神经元背景下描述微观和宏观状态之间的区别，以及捕捉相关隐藏信息度量所需的熵的特征。我们通过离散状态神经元的不可区分重排来讨论熵的数学形式的起源，并展示如何将这些论证扩展到连续大规模神经系统的相空间描述中。最后，我们展示了相空间中的粗粒化操作所代表的神经成像分辨率限制如何根据热力学第二定律导致熵随时间增加。我们希望这本入门读物能支持越来越多将熵用作表征神经成像时间序列和推断脑状态的研究。
