スケール依存複合性の正式な定義と,必要多様性の多スケール法則
Alexander F Siegenfeld1,2, Yaneer Bar-Yam2
1Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
Entropy (Basel, Switzerland)
|August 28, 2025
まとめ
この研究は,アッシュビーの必要な多様性の法則の多次元一般化を導入し,異なるスケールにおけるシステム複雑性のより包括的な理解を可能にします. 新しいフレームワークは,システムの有効性分析の改善のための複雑性プロファイルと複数のスケールの制約を定義します.
科学分野:
- システム理論
- サイバーネティクス
- 情報理論
背景:
- アッシュビーの必要な多様性の法則は,システム理論の基礎的な概念であり,環境に対するシステムの複雑性に基づくシステムの有効性の必要条件を確立します.
- 分析の詳細度やスケールによってシステムの複雑性がどう変化するかは,元の法律では説明されていません.
研究 の 目的:
- 必要な多様性のアッシュビーの法則の多次元的一般化を開発する.
- マルチスケールの複雑性とその制約を特徴づけるための形式主義を導入する.
- 一般的な法則を様々なシステム構造に拡張する.
主な方法:
- 複雑性をスケールの関数として表現する複雑性プロファイルの定義
- システム行動に関する多層制約の公式化.
- 複合性プロフィールの数学分析,合計ルールを含む.
主要な成果:
- 必要な多様性の複数スケールの法則を示す最初の既知の複雑性プロファイルの導入.
- アッシュビーの法則を単一の制約から複数の制約のクラスに一般化する.
- 異なる自由度間のトレードオフを図示する複雑性プロファイルの合計ルールの実証.
結論:
- 提案されたマルチスケールフレームワークは,さまざまなスケールでのシステムの複雑性と有効性を分析するための堅固な方法を提供します.
- 一般化された法則は,システム構造,環境の相互作用,全体的なシステム性能の関係についてより深い洞察を提供します.
- 形式主義は,細分されたコンポーネントや連続した構造を持つものを含む複雑なシステムに適用できます.
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