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第185行： − 自由能最小化等价于最大化参数化变分密度的感觉状态和内部状态之间的互信息(对于一个固定的熵变密度)。以及利用信息理论描述最佳行为的相关处理方法。+ − − − +
→Free energy minimisation and self-organisation 自由能最小化和自组织
Free energy minimisation has been proposed as a hallmark of self-organising systems when cast as [[random dynamical system]]s.<ref>Crauel, H., & Flandoli, F. (1994). [https://www.researchgate.net/profile/Hans_Crauel/publication/227072665_Attractor_for_random_dynamical_systems/links/57c2033708aed246b0fe05b5/Attractor-for-random-dynamical-systems.pdf Attractors for random dynamical systems]. Probab Theory Relat Fields, 100, 365–393.</ref> This formulation rests on a [[Markov blanket]] (comprising action and sensory states) that separates internal and external states. If internal states and action minimise free energy, then they place an upper bound on the entropy of sensory states
Free energy minimisation has been proposed as a hallmark of self-organising systems when cast as [[random dynamical system]]s.<ref>Crauel, H., & Flandoli, F. (1994). [https://www.researchgate.net/profile/Hans_Crauel/publication/227072665_Attractor_for_random_dynamical_systems/links/57c2033708aed246b0fe05b5/Attractor-for-random-dynamical-systems.pdf Attractors for random dynamical systems]. Probab Theory Relat Fields, 100, 365–393.</ref> This formulation rests on a [[Markov blanket]] (comprising action and sensory states) that separates internal and external states. If internal states and action minimise free energy, then they place an upper bound on the entropy of sensory states
自由能最小化被认为是[[自组织系统]]的一个标志。<ref>Crauel, H., & Flandoli, F. (1994). [https://www.researchgate.net/profile/Hans_Crauel/publication/227072665_Attractor_for_random_dynamical_systems/links/57c2033708aed246b0fe05b5/Attractor-for-random-dynamical-systems.pdf Attractors for random dynamical systems]. Probab Theory Relat Fields, 100, 365–393.</ref> 这个公式建立在一个[[马尔可夫毯]]（包括行动和感觉状态）分离内部和外部状态。如果内部状态和行为使自由能最小化，那么它们就给感官状态的熵设置了一个上限。
: <math> \lim_{T\to\infty} \frac{1}{T} \underset{\text{free-action}} {\underbrace{\int_0^T F(s(t),\mu (t))\,dt}} \ge
: <math> \lim_{T\to\infty} \frac{1}{T} \underset{\text{free-action}} {\underbrace{\int_0^T F(s(t),\mu (t))\,dt}} \ge
Free energy minimisation is equivalent to maximising the mutual information between sensory states and internal states that parameterise the variational density (for a fixed entropy variational density). and related treatments using information theory to describe optimal behaviour.
Free energy minimisation is equivalent to maximising the mutual information between sensory states and internal states that parameterise the variational density (for a fixed entropy variational density). and related treatments using information theory to describe optimal behaviour.
自由能最小化相当于最大化感观状态和内部状态之间的互信息，使变分密度参数化（对于固定熵变分密度）。利用信息论描述最优行为的相关处理。
This is because – under [[Ergodic theory|ergodic]] assumptions – the long-term average of surprise is entropy. This bound resists a natural tendency to disorder – of the sort associated with the [[second law of thermodynamics]] and the [[fluctuation theorem]].
This is because – under [[Ergodic theory|ergodic]] assumptions – the long-term average of surprise is entropy. This bound resists a natural tendency to disorder – of the sort associated with the [[second law of thermodynamics]] and the [[fluctuation theorem]].
这是因为在[[遍历理论|遍历]]假设下，惊喜的长期平均值是熵。这个界限抵抗了一种自然的无序倾向，这种无序倾向与[[热力学第二定律]]和[[涨落定理]]有关。
=== Free energy minimisation and Bayesian inference 自由能最小化与贝叶斯推理===
=== Free energy minimisation and Bayesian inference 自由能最小化与贝叶斯推理===