标题： 从费舍尔信息度量中涌现的广义相对论 显示英文标题

标题： Emergent General Relativity from Fisher Information Metric

摘要： 我们从由统计力学系统的概率分布定义的费舍尔信息度规导出爱因斯坦张量。我们发现，当系统的熵数据或谱数据被嵌入经典场作为场强时，该张量自然包含了经典纯量场的能量-动量张量的基本信息。因此，我们可以将爱因斯坦方程视为经典场论背后原始微观系统粗粒化状态的方程。我们对引力的量子化以及各种量子-经典对应关系作了一些评述。 显示英文摘要

摘要： We derive the Einstein tensor from the Fisher information metric that is defined by the probability distribution of a statistical mechanical system. We find that the tensor naturally contains essential information of the energy-momentum tensor of a classical scalar field, when the entropy data or the spectrum data of the system are embedded into the classical field as the field strength. Thus, we can regard the Einstein equation as the equation of coarse-grained states for the original microscopic system behind the classical field theory. We make some remarks on quantization of gravity and various quantum-classical correspondences.