Pith Number

pith:I7QUY4EX

pith:2026:I7QUY4EXIKFOW5SCB63F64SCUL

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Cycle affinity and winding localize eigenvalues of Markov generators

Artemy Kolchinsky, Naruo Ohga, Sosuke Ito

Each complex eigenvalue of a Markov generator is confined to a region set by the affinity of some nonequilibrium cycle and the winding number of its eigenvector.

arxiv:2605.15884 v1 · 2026-05-15 · cond-mat.stat-mech

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Claims

C1strongest claim

we prove that each complex eigenvalue is confined to a region determined by the cycle affinity and the eigenvector ``winding number'' of some nonequilibrium cycle

C2weakest assumption

The localization argument assumes that for every complex eigenvalue there exists at least one nonequilibrium cycle whose affinity and the eigenvector's winding number together define a confining region, an assumption invoked in the main theorem but whose generality across arbitrary multicyclic generators is not obvious from standard Markov theory.

C3one line summary

Complex eigenvalues of Markov generators are localized by cycle affinity and winding numbers, yielding thermodynamic bounds on relaxation modes and proving the Uhl-Seifert ellipse conjecture.

References

48 extracted · 48 resolved · 0 Pith anchors

[1] N.G.VanKampen,Stochasticprocessesinphysicsandchemistry, Vol. 1 (Elsevier, 1992) 1992

[2] Schnakenberg, Network theory of microscopic and macro- scopic behavior of master equation systems, Reviews of Modern physics48, 571 (1976) 1976

[3] Qian, Thermodynamic and kinetic analysis of sensitivity am- plification in biological signal transduction, Biophysical chem- istry105, 585 (2003) 2003

[4] M. Skoge, S. Naqvi, Y. Meir, and N. S. Wingreen, Chemical sensingbynonequilibriumcooperativereceptors,Physicalreview letters110, 248102 (2013) 2013

[5] P. Mehta and D. J. Schwab, Energetic costs of cellular compu- tation, Proceedings of the National Academy of Sciences109, 17978 (2012) 2012

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:23.609286Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47e14c7097428aeb76420fb65f7242a2e1ee717d9726c643f19a182a0cef47f9

Aliases

arxiv: 2605.15884 · arxiv_version: 2605.15884v1 · doi: 10.48550/arxiv.2605.15884 · pith_short_12: I7QUY4EXIKFO · pith_short_16: I7QUY4EXIKFOW5SC · pith_short_8: I7QUY4EX

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/I7QUY4EXIKFOW5SCB63F64SCUL \
  | 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: 47e14c7097428aeb76420fb65f7242a2e1ee717d9726c643f19a182a0cef47f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff17953fb36c0c1bd06bbcb794588e44fccfda434d57d75103d12e10db508d87",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-05-15T12:07:53Z",
    "title_canon_sha256": "ca1e1a61a8ed80d45336ee1f02ce961b3e4f4cdd668db4eb5f8fb7692695bca8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15884",
    "kind": "arxiv",
    "version": 1
  }
}