Pith Number

pith:27YLCN6L

pith:2026:27YLCN6LR3ZI25XQ6QA6TFKEST

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Ergodic Optimization and Ground States: a brief Introduction

Artur O. Lopes

The paper delivers a brief, non-technical overview of ergodic optimization and its relationship to statistical mechanics without new results or proofs.

arxiv:2605.13342 v1 · 2026-05-13 · math.DS · math-ph · math.MP · math.PR

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3 Author claim open · sign in to claim

4 Citations open

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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

Our goal in this short note is to briefly and succinctly describe some basic concepts and properties of Ergodic Optimization for readers unfamiliar with the subject.

C2weakest assumption

That a schematic, non-technical description with selected examples can convey the essential relationship between ergodic optimization and statistical mechanics without technical details or proofs.

C3one line summary

The paper delivers a brief, non-technical overview of ergodic optimization and its relationship to statistical mechanics without new results or proofs.

References

44 extracted · 44 resolved · 0 Pith anchors

[1] Baladi, Positive Transfer Operators and Decay of Correlations, World Scientific (2000) 2000

[2] A. Baraviera, A. O. Lopes and Ph. Thieullen, A Large Deviation Prin- ciple for Gibbs states of H¨ older potentials: the zero temperature case. Stoch. and Dyn. (6), 77-96, (2006) 2006

[3] A. Baraviera, R. Leplaideur and A. O. Lopes, Selection of ground states in the zero temperature limit for a one-parameter family of potentials, SIAM Journal on Appl. Dyn. Systems, Vol. 11, no. 1, 243- 2012

[4] A. Baraviera, R. Leplaideur and A. O. Lopes, Ergodic Optimization, Zero Temperature Limits and the Max-Plus Algebra, XXIX Col´ oquio Brasileiro de Matem´ atica (2013) 15 2013

[5] Bochi, Ergodic optimization of Birkhoff averages and Lyapunov ex- ponents 2018

Receipt and verification

First computed	2026-05-18T02:44:48.378493Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7f0b137cb8ef28d76f0f401e9954494c557983b4b81f76786c0134280d081a7

Aliases

arxiv: 2605.13342 · arxiv_version: 2605.13342v1 · doi: 10.48550/arxiv.2605.13342 · pith_short_12: 27YLCN6LR3ZI · pith_short_16: 27YLCN6LR3ZI25XQ · pith_short_8: 27YLCN6L

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/27YLCN6LR3ZI25XQ6QA6TFKEST \
  | 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: d7f0b137cb8ef28d76f0f401e9954494c557983b4b81f76786c0134280d081a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6534f7e7dd0510121f332c08d943d63c4acf6f3f32e90487d4e3d7bd27b3711a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-13T11:01:49Z",
    "title_canon_sha256": "84e8a8c12ed53f1dc44e5ab7878d657ad632e59b9216e30a7452849fbaf8cfc4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13342",
    "kind": "arxiv",
    "version": 1
  }
}