Backward transfer entropy: Informational measure for detecting hidden Markov models and its interpretations in thermodynamics, gambling and causality

TL;DR

This paper introduces backward transfer entropy as a new measure to detect hidden Markov models and interprets its significance across thermodynamics, gambling, and causality, revealing deep connections between information flow and physical or economic systems.

Contribution

The paper defines backward transfer entropy and explores its physical and practical interpretations, extending the understanding of information flow in complex systems.

Findings

Backward transfer entropy quantifies deviation from hidden Markov models.

It characterizes potential loss of benefits in thermodynamics and gambling.

Reveals connections between thermodynamics, gambling, and information flow.

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.