Wallace Rodrick
Division of Epidemiology, The New York State Psychiatric Institute, New York, NY 10032 United States.
J Theor Biol. 2018 Jan 7;436:72-78. doi: 10.1016/j.jtbi.2017.09.024. Epub 2017 Sep 29.
Cognition most singularly involves choice that reduces uncertainty. Reduction of uncertainty implies the existence of an information source 'dual' to the cognitive process under study. However, information source uncertainty for path-dependent nonergodic systems cannot be described as a conventional Shannon 'entropy' since time averages are not ensemble averages. Nonetheless, the essential nature of information as a form of free energy allows study of nonergodic cognitive systems having complex dynamic topologies whose algebraic expression is in terms of directed homotopy groupoids rather than groups. This permits a significant extension of the Data Rate Theorem linking control and information theories via an analog to the spontaneous symmetry breaking arguments fundamental to modern physics. In addition, the identification of information as a form of free energy enables construction of dynamic empirical Onsager models in the gradient of a classic entropy that can be built from the Legendre transform of even path-dependent information source uncertainties. The methodology provides new analytic tools that should prove useful in understanding failure modes and their dynamics across a broad spectrum of cognitive phenomena, ranging from physiological processes at different scales and levels of organization to critical system automata and institutional economics.
认知最独特地涉及到减少不确定性的选择。不确定性的减少意味着存在一个与正在研究的认知过程“对偶”的信息源。然而，对于路径依赖的非遍历系统，信息源的不确定性不能用传统的香农“熵”来描述，因为时间平均值不是系综平均值。尽管如此，信息作为自由能形式的本质使得能够研究具有复杂动态拓扑结构的非遍历认知系统，其代数表达式是基于有向同伦广群而非群。这允许通过类似于现代物理学中自发对称性破缺论证的方式，对将控制理论和信息理论联系起来的数据速率定理进行重大扩展。此外，将信息识别为自由能的一种形式，能够在经典熵的梯度中构建动态经验昂萨格模型，该模型可以从甚至路径依赖的信息源不确定性的勒让德变换构建。该方法提供了新的分析工具，在理解广泛的认知现象中的故障模式及其动态方面应该会很有用，这些认知现象涵盖从不同尺度和组织层次的生理过程到关键系统自动机和制度经济学。
