Abstract
The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer entropy of the backward time series called the backward transfer entropy, and show that the backward transfer entropy quantifies how far it is from dynamics to a hidden Markov model. Furthermore, we discuss physical interpretations of the backward transfer entropy in completely different settings of thermodynamics for information processing and the gambling with side information. In both settings of thermodynamics and the gambling, the backward transfer entropy characterizes a possible loss of some benefit, where the conventional transfer entropy characterizes a possible benefit. Our result implies the deep connection between thermodynamics and the gambling in the presence of information flow, and that the backward transfer entropy would be useful as a novel measure of information flow in nonequilibrium thermodynamics, biochemical sciences, economics and statistics.
Highlights
In recent studies of a thermodynamic model implementing the Maxwell’s demon[31,32], which reduces the entropy change in a small subsystem by using information, TE has attracted much attention[13,14,15,18,33,34,35,36,37,38]
We proposed that directed measure of information called backward transfer entropy (BTE), which is possibly useful to detect a hidden Markov model (7) and predictive anti-causality (29)
The concept of BTE can provide a clear perspective in the studies of the biochemical sensor and thermodynamics of information, because the difference between TE and dynamic information flow (DIF) has attracted attention recently in these fields[14,35]
Summary
In recent studies of a thermodynamic model implementing the Maxwell’s demon[31,32], which reduces the entropy change in a small subsystem by using information, TE has attracted much attention[13,14,15,18,33,34,35,36,37,38]. From the view point of the statistical hypothesis test, BTE quantifies an anti-causal prediction These fact implies that BTE would be a useful directed measure of information flow as well as TE. Our result reveals the deep connection between two different fields of science, thermodynamics and gambling
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