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Diversidad y similitud de las transferencias y flujos de información en sistemas estocásticos de tiempo continuo
1Institute of Physics, Saratov State University, 155 Moskovskaya Street, Saratov 410012, Russia.
Chaos (Woodbury, N.Y.)
|August 25, 2025
Resumen
Este estudio introduce nuevos cuantificadores de efectos causales dinámicos (DCE) para sistemas estocásticos de tiempo continuo. Estas nuevas medidas capturan el flujo de información y la causalidad, extendiendo el trabajo anterior sobre las cadenas de Markov.
Área de la Ciencia:
- Teoría de los sistemas dinámicos
- Teoría de la información
- Física estadística
Sus antecedentes:
- Los marcos existentes para la causalidad a menudo se centran en tiempos discretos o tipos de sistemas específicos.
- La cuantificación del flujo de información en sistemas estocásticos continuos presenta desafíos únicos.
- Los trabajos anteriores consideraban principalmente las cadenas de Markov, lo que limitaba la aplicabilidad a sistemas dinámicos más amplios.
Objetivo del estudio:
- Extender el marco de los efectos causales dinámicos (DCE) a los sistemas dinámicos estocásticos con tiempo y estado continuos.
- Introducir nuevos DCE informativos, incluidas las tasas de DCE de primer y segundo orden.
- Establecer relaciones analíticas entre estos cuantificadores de causalidad recién definidos.
Principales métodos:
- Aplicación del marco de efectos causales dinámicos (DCE).
- Desarrollo de ECD informativos con tiempo de respuesta finito.
- Introducción y análisis de las tasas de DCE de primer y segundo orden.
- Derivación de las relaciones analíticas entre las diferentes medidas de DCE.
- Validación numérica mediante sistemas de relajación estocástica acoplados.
Principales resultados:
- Se generó una secuencia lógica de una docena de cuantificadores de causalidad informativa para sistemas estocásticos continuos.
- Se introdujeron DCE informativos con tiempo de respuesta finito y sus tasas de DCE correspondientes.
- Relaciones analíticas establecidas entre las ECD informativas estudiadas.
- Se han identificado medidas bien conocidas de transferencia y flujo de información, como la entropía de transferencia, dentro del nuevo marco.
- Se han obtenido valores numéricos típicos y relaciones cuantitativas utilizando sistemas de relajación estocástica acoplados.
Conclusiones:
- El marco DCE extendido proporciona un conjunto completo de herramientas para cuantificar la causalidad en sistemas dinámicos estocásticos continuos.
- Las tasas de DCE recientemente introducidas ofrecen una visión más profunda de la dinámica del flujo de información.
- Los resultados facilitan una comprensión unificada de las diversas medidas de transferencia de información dentro de una sola estructura teórica.
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