具有破态遍历热力学系统的平衡自由能分布
Distribution of equilibrium free energies in a thermodynamic system with broken ergodicity
摘要：
在低温下，宏观复杂系统（例如，$N\sim 10^{23}$相互作用粒子的自旋玻璃）可以分裂成指数数量的$Ω_s \sim \exp({\rm const} \times N)$遍历子空间（热力学状态）。以往的理论研究认为，这种系统的平衡集体行为由其最小自由能量密度的基态热力学态决定，平衡自由能服从指数衰减分布。在这里，我们表明，这些假设不一定是有效的。对于某些复杂系统，平衡自由能值在中间温度范围内可能遵循高斯分布，因此它们的平衡性质由{ \em激发}热力学状态贡献。这一工作将有助于提高我们对自旋玻璃和其他复杂系统平衡态统计力学的理解。
英文摘要：
At low temperatures the configurational phase space of a macroscopic complex system (e.g., a spin-glass) of $N\sim 10^{23}$ interacting particles may split into an exponential number $Ω_s \sim \exp({\rm const} \times N)$ of ergodic sub-spaces (thermodynamic states). Previous theoretical studies assumed that the equilibrium collective behavior of such a system is determined by its ground thermodynamic states of the minimal free-energy density, and that the equilibrium free energies follow the distribution of exponential decay. Here we show that these assumptions are not necessarily valid. For some complex systems, the equilibrium free-energy values may follow a Gaussian distribution within an intermediate temperature range, and consequently their equilibrium properties are contributed by {\em excited} thermodynamic states. This work will help improving our understanding of the equilibrium statistical mechanics of spin-glasses and other complex systems.
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