Temporal irreversibility, often referred to as the arrow of time, is a fundamental concept in statistical mechanics. Markers of irreversibility also provide a powerful characterisation of information processing in biological systems. However, current approaches tend to describe temporal irreversibility in terms of a single scalar quantity, without disentangling the underlying dynamics that contribute to irreversibility. Here we propose a broadly applicable information-theoretic framework to characterise the arrow of time in multivariate time series, which yields qualitatively different types of irreversible information dynamics. This multidimensional characterisation reveals previously unreported high-order modes of irreversibility, and establishes a formal connection between recent heuristic markers of temporal irreversibility and metrics of information processing. We demonstrate the prevalence of high-order irreversibility in the hyperactive regime of a biophysical model of brain dynamics, showing that our framework is both theoretically principled and empirically useful. This work challenges the view of the arrow of time as a monolithic entity, enhancing both our theoretical understanding of irreversibility and our ability to detect it in practical applications.

翻译：时间不可逆性，通常被称为时间之箭，是统计力学中的基本概念。不可逆性的标志也为生物系统中的信息处理提供了强有力的表征。然而，当前的方法倾向于用单一标量来描述时间不可逆性，而未厘清促成不可逆性的潜在动力学。在此，我们提出一个广泛适用的信息论框架，用于刻画多变量时间序列中的时间之箭，该框架能够产生性质不同的不可逆信息动力学类型。这种多维表征揭示了先前未被报道的高阶不可逆性模式，并建立了近期时间不可逆性启发式标记与信息处理度量之间的形式化关联。我们通过一个脑动力学生物物理模型在过度活跃状态下的表现，证明了高阶不可逆性的普遍存在，表明我们的框架既具有理论原则性，又具有实际应用价值。这项工作挑战了将时间之箭视为单一实体的观点，既深化了我们对不可逆性的理论理解，也增强了我们在实际应用中检测不可逆性的能力。