連続時間ストキャスティックシステムにおける情報転送とフローの多様性と類似性
1Institute of Physics, Saratov State University, 155 Moskovskaya Street, Saratov 410012, Russia.
Chaos (Woodbury, N.Y.)
|August 25, 2025
まとめ
この研究は,連続時間ストキャスティックシステムの新しいダイナミック因果効果 (DCE) 定量化器を導入します. マルコフ連鎖に関する以前の研究を拡張し,情報フローと因果関係を捉えます.
科学分野:
- ダイナミックシステム理論
- 情報理論
- 統計物理学
背景:
- 現存する因果関係に関する枠組みは,しばしば離散的な時間や特定のシステムタイプに焦点を当てている.
- 継続的なストキャスティックシステムにおける情報フローの量化は,ユニークな課題を提示します.
- 以前の研究は主にマルコフ連鎖を考慮し,より広範な動的システムへの適用を制限していた.
研究 の 目的:
- ダイナミック・カザル・エフェクト (DCE) の枠組みを,連続した時間と状態を持つストキャスティック・ダイナミック・システムに拡張する.
- 第"級と第2級のDCE率を含む新しい情報DCEを導入する.
- これらの新たに定義された因果関係量化器の間の分析的関係を確立する.
主な方法:
- ダイナミックな因果関係 (DCEs) フレームワークの適用
- 限られた応答時間を持つ情報DCEの開発.
- 第1次および第2次DCE率の導入と分析
- 異なるDCE測定値の間の分析的関係を導出する.
- カップルストキャスティック・リラクゼーション・システムを用いた数値検証
主要な成果:
- 連続したストキャスティックシステムの12の情報因果関係定量器の論理シーケンスが生成されました.
- 限られた応答時間とそれに対応するDCE率を導入した.
- 研究された情報DCEの間の分析的関係が確立された.
- 新しい枠組みの中で,転送エントロピーのような,よく知られた情報転送とフローの測定値を特定しました.
- 組み合わせたストキャスティック・リラクゼーション・システムを用いて得られた典型的な数値と量的な関係.
結論:
- 拡張されたDCEフレームワークは,連続したストキャスティック動的システムにおける因果関係を定量化するための包括的なツールセットを提供します.
- 新しく導入されたDCEレートは,情報流動のダイナミクスをより深く理解できます.
- 発見は,単一の理論的構造の中で,さまざまな情報転送措置の統一された理解を容易にする.
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