Quantum thermalization and average entropy of a subsystem
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| Format: | Preprint |
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2025
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| _version_ | 1866918155006246912 |
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| author | Mishra, Smitarani Sahoo, Shaon |
| author_facet | Mishra, Smitarani Sahoo, Shaon |
| contents | 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 $\mathcal{H}_E$ corresponding to a narrow energy shell centered at energy $E$. We find that the average entropy is $\overline{S}_{1} \simeq \ln d_1$, where $d_1$ represents first subsystem's effective number of states relevant to the energy scale $E$. If $d_E = \dim{(\mathcal{H}_E)}$ and $D$ ($D_1$) is the Hilbert space dimension of the full system (first subsystem), we estimate that $d_1 \simeq D_1^γ$, where $γ= \ln (d_E) / \ln (D)$ for nonintegrable (chaotic) systems and $γ< \ln (d_E) / \ln (D)$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_19896 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum thermalization and average entropy of a subsystem Mishra, Smitarani Sahoo, Shaon Quantum Physics 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 $\mathcal{H}_E$ corresponding to a narrow energy shell centered at energy $E$. We find that the average entropy is $\overline{S}_{1} \simeq \ln d_1$, where $d_1$ represents first subsystem's effective number of states relevant to the energy scale $E$. If $d_E = \dim{(\mathcal{H}_E)}$ and $D$ ($D_1$) is the Hilbert space dimension of the full system (first subsystem), we estimate that $d_1 \simeq D_1^γ$, where $γ= \ln (d_E) / \ln (D)$ for nonintegrable (chaotic) systems and $γ< \ln (d_E) / \ln (D)$ 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. |
| title | Quantum thermalization and average entropy of a subsystem |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2506.19896 |