Prokopenko Mikhail, Lizier Joseph T
1] CSIRO Computational Informatics, PO Box 76, Epping, NSW 1710, Australia [2] Department of Computing, Macquarie University, E6A Level 3, Eastern Rd, Macquarie Park, NSW 2113, Australia [3] School of Physics, University of Sydney, Physics Rd, Camperdown NSW 2050, Australia.
CSIRO Computational Informatics, PO Box 76, Epping, NSW 1710, Australia.
Sci Rep. 2014 Jun 23;4:5394. doi: 10.1038/srep05394.
Transfer entropy is a recently introduced information-theoretic measure quantifying directed statistical coherence between spatiotemporal processes, and is widely used in diverse fields ranging from finance to neuroscience. However, its relationships to fundamental limits of computation, such as Landauer's limit, remain unknown. Here we show that in order to increase transfer entropy (predictability) by one bit, heat flow must match or exceed Landauer's limit. Importantly, we generalise Landauer's limit to bi-directional information dynamics for non-equilibrium processes, revealing that the limit applies to prediction, in addition to retrodiction (information erasure). Furthermore, the results are related to negentropy, and to Bremermann's limit and the Bekenstein bound, producing, perhaps surprisingly, lower bounds on the computational deceleration and information loss incurred during an increase in predictability about the process. The identified relationships set new computational limits in terms of fundamental physical quantities, and establish transfer entropy as a central measure connecting information theory, thermodynamics and theory of computation.
转移熵是最近引入的一种信息论度量，用于量化时空过程之间的定向统计相干性，并且在从金融到神经科学等不同领域中得到广泛应用。然而，它与诸如兰道尔极限等基本计算极限之间的关系仍然未知。在此我们表明，为了将转移熵（可预测性）提高一位，热流必须匹配或超过兰道尔极限。重要的是，我们将兰道尔极限推广到非平衡过程的双向信息动力学，揭示该极限不仅适用于追溯（信息擦除），也适用于预测。此外，这些结果与负熵、布雷默曼极限以及贝肯斯坦界相关，或许令人惊讶的是，它们给出了在提高对该过程的可预测性期间所产生的计算减速和信息损失的下限。所确定的这些关系依据基本物理量设定了新的计算极限，并将转移熵确立为连接信息论、热力学和计算理论的核心度量。
