尺度不变系统的Fisher热力学：Zipf定律作为无尺度理想气体的平衡态
Fisher-based thermodynamics for scale-invariant systems: Zipf's Law as an equilibrium state of a scale-free ideal gas
摘要：
我们提出了一个基于极端信息原理的标度不变系统的热力学公式。我们创建一个类比这些系统和众所周知的气体和流体的热力学，并研究作为一个令人信服的情况下，非相互作用的系统-无标度理想气体-提出一些经验证据的选举结果，城市人口和物理学期刊的总引用，证实它的存在。经验类的普遍性称为齐普夫定律是来自第一原理：我们表明，这类特殊的幂律可以理解为密度分布的平衡态的无标度理想气体，而不同指数的幂律产生于平衡和非平衡态。我们还预测对数正态分布的外观作为一个和谐的约束系统的平衡密度，并最终推导出这些系统的等效微观描述。
英文摘要：
We present a thermodynamic formulation for scale-invariant systems based on the principle of extreme information. We create an analogy between these systems and the well-known thermodynamics of gases and fluids, and study as a compelling case the non-interacting system -the scale-free ideal gas- presenting some empirical evidences of electoral results, city population and total cites of Physics journals that confirm its existence. The empirical class of universality known as Zipf's law is derived from first principles: we show that this special class of power law can be understood as the density distribution of an equilibrium state of the scale-free ideal gas, whereas power laws of different exponent arise from equilibrium and non-equilibrium states. We also predict the appearance of the log-normal distribution as the equilibrium density of a harmonically constrained system, and finally derive an equivalent microscopic description of these systems.
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