2025/06/24 by Mishra, Smitarani, Sahoo, Shaon · 1 citation
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2506.19896
Page's seminal result on the average von Neumann (VN) entropy does not immediately apply to realistic many-body systems which are restricted to physically relevant smaller subspaces. We investigate here the VN entropy averaged over the pure states in the subspace HE corresponding to a narrow energy shell centered at energy E. We find that the average entropy is S1 ≃ ln d1, where d1 represents first subsystem's effective number of states relevant to the energy scale E. If dE = dim(HE) and D (D1) is the Hilbert space dimension of the full system (first subsystem), we estimate that d1 ≃ D1γ, where γ= ln (dE) / ln (D) for nonintegrable (chaotic) systems and γ< ln (dE) / ln (D) for integrable systems. This result can be reinterpreted as a volume-law of entropy, where the volume-law coefficient depends on the density-of-states for nonintegrable systems, and remains below the maximal possible value for integrable systems. We numerically analyze a spin model to substantiate our main results.