Pith Number

pith:YQRMJB4L

pith:2025:YQRMJB4LGXKJGEZWY6NVHFWVL3

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Planckian bound on quantum dynamical entropy

Xiangyu Cao

Monitoring thermal fluctuations in many-body quantum systems yields an entropy growth rate bounded by a universal Planckian value.

arxiv:2507.20914 v4 · 2025-07-28 · quant-ph · cond-mat.stat-mech

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We conjecture a universal Planckian bound for the entropy rate.

C2weakest assumption

The entropy rate computation and bound conjecture rely on taking the thermodynamic limit and long-time limit for a generic many-body system whose thermal fluctuations of an extensive observable produce nonzero information gain away from classical or large-N regimes.

C3one line summary

A simplified version of quantum dynamical entropy is introduced, its growth rate is computed from correlation functions in the thermodynamic limit, and a Planckian bound on the rate is conjectured.

References

88 extracted · 88 resolved · 1 Pith anchors

[1] A. N. Kolmogorov, A new metric invariant of tran- sient dynamical systems and automorphisms in lebesgue spaces, Dokl. Akad. Nauk SSSR (1958) 1958

[2] Y. G. Sinai, On the notion of entropy of a dynamical system, in Dokl. Akad. Nauk SSSR , Vol. 124 (1959) pp. 768–771 1959

[3] Y. G. Sinai, Kolmogorov-sinai entropy, Scholarpedia 4, 2034 (2009) 2034

[4] Walters, An introduction to ergodic theory , Vol 2000

[5] B. Hasselblatt and Y. Pesin, Pesin entropy formula, Scholarpedia 3, 3733 (2008), revision #185293 2008

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

Planckian dissipation from classical hydrodynamics

Receipt and verification

First computed	2026-05-28T02:04:42.125993Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c422c4878b35d4931336c79b5396d55ec09b17907086c7c8553bd1edbeef9d0f

Aliases

arxiv: 2507.20914 · arxiv_version: 2507.20914v4 · doi: 10.48550/arxiv.2507.20914 · pith_short_12: YQRMJB4LGXKJ · pith_short_16: YQRMJB4LGXKJGEZW · pith_short_8: YQRMJB4L

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YQRMJB4LGXKJGEZWY6NVHFWVL3 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c422c4878b35d4931336c79b5396d55ec09b17907086c7c8553bd1edbeef9d0f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9403b57d0afefad74d581f43c1db820c4efa156ccc3c0286db5149ce454c2cdb",
    "cross_cats_sorted": [
      "cond-mat.stat-mech"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2025-07-28T15:09:57Z",
    "title_canon_sha256": "a54e8241d9c694017f3a600aa60b6c7aa2ab09b261f4a1af38a746317763a89c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.20914",
    "kind": "arxiv",
    "version": 4
  }
}