Thermal fluctuations are not large enough to lead to state changes in granular materials. However, in many cases, such materials do achieve reproducible bulk properties, suggesting that they are controlled by an underlying statistical mechanics analogous to thermodynamics. While themodynamic descriptions of granular materials have been explored, they have not yet been concretely connected to their underlying statistical mechanics. We make this connection concrete by providing a first principles derivation of the multiplicity and thus the entropy of the force networks in granular packings. We directly measure the multiplicity of force networks using a protocol based on the phase space volume of allowed force configurations. Analogous to Planck’s constant, we find a scale factor, $h_f$, that discretizes this phase space volume into a multiplicity. To determine this scale factor, we measure angoricity over a wide range of pressures using the method of overlapping histograms and find that in the absence of a fundamental quantum scale it is set solely by the system size and dimensionality. This concretely links thermodynamic approaches of angoricity with the microscopic multiplicity of the Force Network Ensemble.

中文翻译：

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干扰中力构熵的直接测量

热涨落不足以导致粒状材料的状态变化。但是，在许多情况下，此类材料的确具有可重现的体积特性，这表明它们受类似于热力学的基本统计力学控制。虽然已经探索了颗粒材料的热力学描述，但它们尚未与潜在的统计机制具体联系起来。我们通过提供多重性的第一个原理推导这种连接，从而推导了粒状填料中力网络的熵。我们基于允许的力配置的相空间量，使用协议直接测量力网络的多样性。类似于普朗克常数，我们找到一个比例因子，$H_F$，将这个相空间体积离散化为多重。为了确定该比例因子，我们使用重叠直方图的方法在很大的压力范围内测量了电子度，发现在没有基本量子比例的情况下，它仅由系统大小和维数设置。具体来说，这就是将热力学的热力学方法与力网络集成的微观多样性联系起来。