主题：【原创】围绕脑科学而发生的若干玄想 -- 鸿乾

the paper you quoted is a good one, worth reading a couple of times and the referenced other ones,

in terms of their methodology:

1) getting information at system level or field level, are we near or moving towards a "canonical (平衡正則) system"? or field analysis of the ant folks

2)

then do "path" analysis to get further into operational level, such as how many path, and which path in terms of 測度 / 機率 density distribution, the ant is moving around, and once we have those information, we could tell ant: baby, we have got you.

1. 溫度 is a system level concept, and normally you can only define and measure 溫度 near/towards a "canonical (平衡正則) system"

2. once we have 溫度, we basically can do partitions @energy level, calculate entropy etc, with the subject heat system modeled and assumed as a heat 标量场, with 动力学 tricks such as 梯度, etc

3. the following article gives shows the common methodlogy behind

费曼路徑積分 vs 马尔可夫模型

as the auther said, 在量子电动力学的振幅是复number/complex number的，with 幅度和相位，可靠性马尔可夫模型 only deals with 实number and there is no 相位;

but with a lower order approximation of a "canonical (平衡正則) system" of the 可靠性 analysis , the author could still 積分疊加 all the 马尔可夫 path, as in 费曼路徑積分

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. a google translation

所以，在这个简单的可靠性模型的上下文中，最低阶近似中，我们可以表示沿每一个可能的路径的转移速率的总和的产品的转移概率。不用说了，有更好的方法来评估的概率马尔可夫模型，但这种原油技术有趣的是，由于它的相似，至少在形式上，振幅在费曼的量子电动力学方法的过渡产品的总和。另一方面，也有一些显着的差异。首先，在量子电动力学的振幅是复杂的，既具有幅度和相位，而在可靠性模型的转换率是纯粹的实部和没有相位。第二，我们考虑的是可靠性模型，而专门的，在这个意义上，每一个路径从一个状态到另一个包括相同数量的单个转换。例如，从状态1到状态8的每个路径包括正好是三个转换。正因为如此，最低阶近似的贡献各路径的时间是相同的顺序为每个其他路径。

Feynman's Ants - MathPages

mathpages.com/home/kmath320/kmath320.htm

According to Feynman, the second ant follows the first path, but sometimes .... The lowest-order approximation of the probability of State 5 is given by the integral ...

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Maximum entropy production and the fluctuation theorem

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R C Dewar

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LETTER TO THE EDITOR

Recently the author used an information theoretical formulation of non-equilibrium statistical mechanics (MaxEnt) to derive the fluctuation theorem (FT) concerning the probability of second law violating phase-space paths. A less rigorous argument leading to the variational principle of maximum entropy production (MEP) was also given. Here a more rigorous and general mathematical derivation of MEP from MaxEnt is presented, and the relationship between MEP and the FT is thereby clarified. Specifically, it is shown that the FT allows a general orthogonality property of maximum information entropy to be extended to entropy production itself, from which MEP then follows. The new derivation highlights MEP and the FT as generic properties of MaxEnt probability distributions involving anti-symmetric constraints, independently of any physical interpretation. Physically, MEP applies to the entropy production of those macroscopic fluxes that are free to vary under the imposed constraints, and corresponds to selection of the most probable macroscopic flux configuration. In special cases MaxEnt also leads to various upper bound transport principles. The relationship between MaxEnt and previous