On Thermodynamic Interpretation of Transfer Entropy

Prokopenko, Mikhail; Lizier, Joseph T.; Price, D. C.

doi:10.3390/e15020524

Cited by 73 publications

(72 citation statements)

References 57 publications

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“…In what follows, we compare the thermodynamic interpretation of Schreiber's transfer entropy as presented in [24,25] with the Liang-Kleeman measure of information transfer after having emphasized its formal analogy with the Horowitz-Esposito thermodynamic formalism.…”

Section: A Thermodynamic Comparisonmentioning

confidence: 99%

“…For an interesting outline of general differences between transfer entropy and information flow defined via a time-shifted mutual information, we refer to [22]. For relatively recent thermodynamic interpretations of transfer entropy, we refer to [24,25].…”

Section: A Thermodynamic Comparisonmentioning

confidence: 99%

“…Furthermore, assuming a Boltzmann entropic expression for the Shannon entropy, Prokopenko et al. arrive at the proportionality between local transfer entropy t Y →X and external entropy production ∆S ext in the additional working hypothesis of small fluctuations near equilibrium [25],…”

Section: A the Liang-kleeman Approach: Thermodynamic Argumentsmentioning

confidence: 99%

“…This first point sets the Liang-Kleeman analysis on more foundational grounds and, in addition, exhibits its similarity with the Horowitz-Esposito thermodynamic analysis of information flow. Second, we compare the foundationally strengthened Liang-Kleeman notion of information transfer with that provided by Schreiber, after having briefly discussed the physical [24] and thermodynamical [25] interpretations of the latter. This second point improves our understanding of the differences between the two notions from a more fundamental point of view [22].…”

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confidence: 99%

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Thermodynamic aspects of information transfer in complex dynamical systems

2016

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From the Horowitz-Esposito stochastic thermodynamical description of information flows in dynamical systems [J. M. Horowitz and M. Esposito, Phys. Rev. X4, 031015 (2014)], it is known that while the second law of thermodynamics is satisfied by a joint system, the entropic balance for the subsystems is adjusted by a term related to the mutual information exchange rate between the two subsystems. In this article, we present a quantitative discussion of the conceptual link between the Horowitz-Esposito analysis and the Liang-Kleeman work on information transfer between dynamical system components [X. S. Liang and R. Kleeman, Phys. Rev. Lett. 95, 244101 (2005)]. In particular, the entropic balance arguments employed in the two approaches are compared. Notwithstanding all differences between the two formalisms, our work strengthens the Liang-Kleeman heuristic balance reasoning by showing its formal analogy with the recent Horowitz-Esposito thermodynamic balance arguments.

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Section: A Thermodynamic Comparisonmentioning

confidence: 99%

Section: A Thermodynamic Comparisonmentioning

confidence: 99%

Section: A the Liang-kleeman Approach: Thermodynamic Argumentsmentioning

confidence: 99%

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confidence: 99%

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Thermodynamic aspects of information transfer in complex dynamical systems

2016

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“…It is worth mentioning that Granger causality and transfer entropy are equivalent for Gaussian distributions according to Barnett et al [10]. After transfer entropy was proposed, it has been widely used in diverse fields, such as statistics [11,12], dynamical systems [13][14][15], social networks [16], physiology [17][18][19], the study of cellular automata in computer science [20,21], and so on.…”

Section: Introductionmentioning

confidence: 99%

A Study of the Transfer Entropy Networks on Industrial Electricity Consumption

Yao

Kuang

Lin

et al. 2017

Entropy

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Abstract:We study information transfer routes among cross-industry and cross-region electricity consumption data based on transfer entropy and the MST (Minimum Spanning Tree) model. First, we characterize the information transfer routes with transfer entropy matrixes, and find that the total entropy transfer of the relatively developed Guangdong Province is lower than others, with significant industrial cluster within the province. Furthermore, using a reshuffling method, we find that driven industries contain much more information flows than driving industries, and are more influential on the degree of order of regional industries. Finally, based on the Chu-Liu-Edmonds MST algorithm, we extract the minimum spanning trees of provincial industries. Individual MSTs show that the MSTs follow a chain-like formation in developed provinces and star-like structures in developing provinces. Additionally, all MSTs with the root of minimal information outflow industrial sector are of chain-form.

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Information theoretical approach to discovering solar wind drivers of the outer radiation belt

et al. 2016

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The solar wind‐magnetosphere system is nonlinear. The solar wind drivers of geosynchronous electrons with energy range of 1.8–3.5 MeV are investigated using mutual information, conditional mutual information (CMI), and transfer entropy (TE). These information theoretical tools can establish linear and nonlinear relationships as well as information transfer. The information transfer from solar wind velocity (Vsw) to geosynchronous MeV electron flux (Je) peaks with a lag time of 2 days. As previously reported, Je is anticorrelated with solar wind density (nsw) with a lag of 1 day. However, this lag time and anticorrelation can be attributed at least partly to the Je(t + 2 days) correlation with Vsw(t) and nsw(t + 1 day) anticorrelation with Vsw(t). Analyses of solar wind driving of the magnetosphere need to consider the large lag times, up to 3 days, in the (Vsw, nsw) anticorrelation. Using CMI to remove the effects of Vsw, the response of Je to nsw is 30% smaller and has a lag time < 24 h, suggesting that the MeV electron loss mechanism due to nsw or solar wind dynamic pressure has to start operating in < 24 h. nsw transfers about 36% as much information as Vsw (the primary driver) to Je. Nonstationarity in the system dynamics is investigated using windowed TE. When the data are ordered according to transfer entropy value, it is possible to understand details of the triangle distribution that has been identified between Je(t + 2 days) versus Vsw(t).

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On Thermodynamic Interpretation of Transfer Entropy

Cited by 73 publications

References 57 publications

Thermodynamic aspects of information transfer in complex dynamical systems

Thermodynamic aspects of information transfer in complex dynamical systems

A Study of the Transfer Entropy Networks on Industrial Electricity Consumption

Information theoretical approach to discovering solar wind drivers of the outer radiation belt

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