爆炸相空间的统计力学：本体开放系统
Statistical mechanics of exploding phase spaces: Ontic open systems
摘要：
对于某些类型的复杂系统，例如生物学和神经科学中遇到的那些系统，相空间的体积可以随着自由度的数量而超指数地（“爆炸性地”）增长，其中组件相互作用并产生新的涌现状态。标准的系综理论可能会崩溃，正如我们在一个简单的模型中所展示的那样，这个模型让人想起新的集体状态出现的复杂系统。我们提出了一个公理定义的熵，并认为它是广泛的微正则，等概率，和规范（最大熵）合奏超指数增长的相空间。这种熵在确定概率度量时可能是有用的，类似于统计力学如何通过最大化熵来建立统计系综。
英文摘要：
The volume of phase space may grow super-exponentially ("explosively") with the number of degrees of freedom for certain types of complex systems such as those encountered in biology and neuroscience, where components interact and create new emergent states. Standard ensemble theory can break down as we demonstrate in a simple model reminiscent of complex systems where new collective states emerge. We present an axiomatically defined entropy and argue that it is extensive in the micro-canonical, equal probability, and canonical (max-entropy) ensemble for super-exponentially growing phase spaces. This entropy may be useful in determining probability measures in analogy with how statistical mechanics establishes statistical ensembles by maximising entropy.
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