Pith Number

pith:H56P2JTV

pith:2026:H56P2JTVSYLL3NSZXVBOT566JX

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Steady-State Equilibrium and Nonequilibrium Noisy Network Dynamics

Pik-Yin Lai

Noisy networks reach equilibrium only when their connections and noise covariances satisfy several equivalent symmetry conditions, which also yield a general fluctuation-dissipation relation for non-equilibrium cases.

arxiv:2604.12225 v2 · 2026-04-14 · cond-mat.stat-mech

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Claims

C1strongest claim

Several equivalent conditions are derived for the dynamics of the noisy network at equilibrium. In particular, non-equilibrium steady state (NESS) dynamics are analyzed in terms of the steady-state probability current and the drift velocity relative to the effective potential surface. Furthermore, a general fluctuation-dissipation relation is derived for the general non-equilibrium noisy network dynamics.

C2weakest assumption

The network possesses a stable, noise-free steady state around which the fluctuating dynamics can be linearized; the analysis relies on this linearization and on the existence of an effective potential surface for the NESS case.

C3one line summary

Noisy directed networks reach equilibrium under specific symmetries of connections and noise covariances; non-equilibrium steady states are characterized by probability currents and drift velocities, with a general fluctuation-dissipation relation derived that includes overdamped Brownian dynamics.

Receipt and verification

First computed	2026-06-10T01:10:01.067719Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3f7cfd26759616bdb659bd42e9f7de4deb4f6303f793b3f9e35f556b0540de2d

Aliases

arxiv: 2604.12225 · arxiv_version: 2604.12225v2 · doi: 10.48550/arxiv.2604.12225 · pith_short_12: H56P2JTVSYLL · pith_short_16: H56P2JTVSYLL3NSZ · pith_short_8: H56P2JTV

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/H56P2JTVSYLL3NSZXVBOT566JX \
  | 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: 3f7cfd26759616bdb659bd42e9f7de4deb4f6303f793b3f9e35f556b0540de2d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a86efe3ff7e6d7402df0397eccb200957d81a3b48100ef96c5f310e379791a0",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-04-14T03:03:12Z",
    "title_canon_sha256": "2148ce6668f060c8fab8dea6218d4cb24205168e2d5a8165317ed53f7fae00a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.12225",
    "kind": "arxiv",
    "version": 2
  }
}