Emergent General Relativity from Fisher Information Metric

2013/10/07 by Hiroaki Matsueda, Matsueda, Hiroaki · 4 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #cond-mat.stat-mech #gr-qc #hep-th

paper · pdf · doi:10.48550/arxiv.1310.1831

20 pages

openalex publication_date 2013/10/07 · arxiv created 2013/12/26 · arxiv updated 2013/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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