dorsal/arxiv
View SchemaUniversal role of correlation entropy in critical phenomena
| Authors | Shi-Jian Gu, Chang-Pu Sun, Hai-Qing Lin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0605164 |
| URL | https://arxiv.org/abs/quant-ph/0605164 |
| DOI | 10.1088/1751-8113/41/2/025002 |
| Journal | J. Phys. A: Math. Theor. 41, 025002 (2008). |
Abstract
In statistical physics, if we successively divide an equilibrium system into two parts, we will face a situation that, within a certain length $\xi$, the physics of a subsystem is no longer the same as the original system. Then the extensive properties of the thermal entropy $S($AB$)= S($A$)+S($B$)$ is violated. This observation motivates us to introduce the concept of correlation entropy between two points, as measured by mutual information in the information theory, to study the critical phenomena. A rigorous relation is established to display some drastic features of the non-vanishing correlation entropy of the subsystem formed by any two distant particles with long-range correlation. This relation actually indicates the universal role of the correlation entropy in understanding critical phenomena. We also verify these analytical studies in terms of two well-studied models for both the thermal and quantum phase transitions: two-dimensional Ising model and one-dimensional transverse field Ising model. Therefore, the correlation entropy provides us with a new physical intuition in critical phenomena from the point of view of the information theory.
{
"annotation_id": "082acb7c-2e27-4374-a7c1-ba4858401a56",
"date_created": "2026-03-02T18:02:27.662000Z",
"date_modified": "2026-03-02T18:02:27.662000Z",
"file_hash": "83d800dd2b02afee04ff1073dd0d1f1afcc4273a473f2550c0b4f2feb5057683",
"private": false,
"record": {
"abstract": "In statistical physics, if we successively divide an equilibrium system into\ntwo parts, we will face a situation that, within a certain length $\\xi$, the\nphysics of a subsystem is no longer the same as the original system. Then the\nextensive properties of the thermal entropy $S($AB$)= S($A$)+S($B$)$ is\nviolated. This observation motivates us to introduce the concept of correlation\nentropy between two points, as measured by mutual information in the\ninformation theory, to study the critical phenomena. A rigorous relation is\nestablished to display some drastic features of the non-vanishing correlation\nentropy of the subsystem formed by any two distant particles with long-range\ncorrelation. This relation actually indicates the universal role of the\ncorrelation entropy in understanding critical phenomena. We also verify these\nanalytical studies in terms of two well-studied models for both the thermal and\nquantum phase transitions: two-dimensional Ising model and one-dimensional\ntransverse field Ising model. Therefore, the correlation entropy provides us\nwith a new physical intuition in critical phenomena from the point of view of\nthe information theory.",
"arxiv_id": "quant-ph/0605164",
"authors": [
"Shi-Jian Gu",
"Chang-Pu Sun",
"Hai-Qing Lin"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech"
],
"doi": "10.1088/1751-8113/41/2/025002",
"journal_ref": "J. Phys. A: Math. Theor. 41, 025002 (2008).",
"title": "Universal role of correlation entropy in critical phenomena",
"url": "https://arxiv.org/abs/quant-ph/0605164"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "624cb7e3-3878-4d11-97e4-4518b0063a85",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}