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第218行： − 通常，定义自由能的生成模型是非线性和层次化的(就像大脑中的皮层层次)。广义滤波的特殊情况包括卡尔曼滤波，这在形式上等同于预测编码——一个流行的比喻信息在大脑中的传递。在层次模型中，预测编码涉及到反复出现的上升(自下而上)预测错误和下降(自上而下)预测，这与感觉和运动系统的解剖学和生理学一致。+ − − +
→Free energy minimisation and thermodynamics 自由能最小化与热力学
Usually, the generative models that define free energy are non-linear and hierarchical (like cortical hierarchies in the brain). Special cases of generalised filtering include Kalman filtering, which is formally equivalent to predictive coding – a popular metaphor for message passing in the brain. Under hierarchical models, predictive coding involves the recurrent exchange of ascending (bottom-up) prediction errors and descending (top-down) predictions that is consistent with the anatomy and physiology of sensory and motor systems.
Usually, the generative models that define free energy are non-linear and hierarchical (like cortical hierarchies in the brain). Special cases of generalised filtering include Kalman filtering, which is formally equivalent to predictive coding – a popular metaphor for message passing in the brain. Under hierarchical models, predictive coding involves the recurrent exchange of ascending (bottom-up) prediction errors and descending (top-down) predictions that is consistent with the anatomy and physiology of sensory and motor systems.
通常，定义自由能的生成模型是非线性和层次化的（就像大脑中的皮层层次结构）。广义滤波的特例包括Kalman滤波，它在形式上等同于预测编码（predictive coding）——大脑中信息传递的一个流行隐喻。在层次模型下，预测编码涉及到上升（自下而上）预测错误和下降（自上而下）预测的反复交换，这与感觉和运动系统的解剖和生理学是一致的。
Variational free energy is an information theoretic functional and is distinct from thermodynamic (Helmholtz) [[Helmholtz free energy|free energy]].<ref>Evans, D. J. (2003). [http://rscweb.anu.edu.au/~evans/papers/NEFET.pdf A non-equilibrium free energy theorem for deterministic systems]. Molecular Physics , 101, 15551–4.</ref> However, the complexity term of variational free energy shares the same fixed point as Helmholtz free energy (under the assumption the system is thermodynamically closed but not isolated). This is because if sensory perturbations are suspended (for a suitably long period of time), complexity is minimised (because accuracy can be neglected). At this point, the system is at equilibrium and internal states minimise Helmholtz free energy, by the [[principle of minimum energy]].<ref>Jarzynski, C. (1997). [https://arxiv.org/abs/cond-mat/9610209 Nonequilibrium equality for free energy differences]. Phys. Rev. Lett., 78, 2690.</ref>
Variational free energy is an information theoretic functional and is distinct from thermodynamic (Helmholtz) [[Helmholtz free energy|free energy]].<ref>Evans, D. J. (2003). [http://rscweb.anu.edu.au/~evans/papers/NEFET.pdf A non-equilibrium free energy theorem for deterministic systems]. Molecular Physics , 101, 15551–4.</ref> However, the complexity term of variational free energy shares the same fixed point as Helmholtz free energy (under the assumption the system is thermodynamically closed but not isolated). This is because if sensory perturbations are suspended (for a suitably long period of time), complexity is minimised (because accuracy can be neglected). At this point, the system is at equilibrium and internal states minimise Helmholtz free energy, by the [[principle of minimum energy]].<ref>Jarzynski, C. (1997). [https://arxiv.org/abs/cond-mat/9610209 Nonequilibrium equality for free energy differences]. Phys. Rev. Lett., 78, 2690.</ref>
变分自由能是一种信息论泛函，不同于热力学（亥姆霍兹Helmholtz）[[Helmholtz自由能|自由能]]。<ref>Evans, D. J. (2003). [http://rscweb.anu.edu.au/~evans/papers/NEFET.pdf A non-equilibrium free energy theorem for deterministic systems]. Molecular Physics , 101, 15551–4.</ref>然而，变分自由能的复杂性项与Helmholtz自由能具有相同的不动点（假设系统是热力学封闭而非孤立的）。这是因为如果感官干扰被暂停（一段适当长的时间），复杂性被最小化（因为准确度可以忽略）。此时，系统处于平衡状态，内部状态根据[[最小能量原理]]使亥姆霍兹自由能最小化。
=== Free energy minimisation and information theory 自由能最小化与信息论===
=== Free energy minimisation and information theory 自由能最小化与信息论===