Thermodynamic aspects of information transfer in complex dynamical systems

Cafaro, Carlo; Ali, S. A.; Giffin, Adom

doi:10.1103/physreve.93.022114

Cited by 22 publications

(20 citation statements)

References 33 publications

(81 reference statements)

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“…In particular, the so-called generalized Landauer's principle [69,97,98] states that, given a system coupled to a heat bath at temperature T , any process that reduces the entropy of the system by n bits must release at least n · k B T ln 2 of energy as heat (alternatively, at most n · k B T ln 2 of heat can be absorbed by any process that increases entropy by n bits). It has also been shown that in certain scenarios, heat must be generated in order to acquire syntactic information, whether mutual information [34,[99][100][101], transfer entropy [102][103][104][105][106], or other measures [107][108][109][110][111].…”

Section: Nonequilibrium Statistical Physicsmentioning

confidence: 99%

Semantic information, autonomous agency and non-equilibrium statistical physics

2018

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Shannon information theory provides various measures of so-called "syntactic information", which reflect the amount of statistical correlation between systems. In contrast, the concept of "semantic information" refers to those correlations which carry significance or "meaning" for a given system. Semantic information plays an important role in many fields, including biology, cognitive science, and philosophy, and there has been a long-standing interest in formulating a broadly applicable and formal theory of semantic information. In this paper we introduce such a theory. We define semantic information as the syntactic information that a physical system has about its environment which is causally necessary for the system to maintain its own existence. "Causal necessity" is defined in terms of counter-factual interventions which scramble correlations between the system and its environment, while "maintaining existence" is defined in terms of the system's ability to keep itself in a low entropy state. We also use recent results in nonequilibrium statistical physics to analyze semantic information from a thermodynamic point of view. Our framework is grounded in the intrinsic dynamics of a system coupled to an environment, and is applicable to any physical system, living or otherwise. It leads to formal definitions of several concepts that have been intuitively understood to be related to semantic information, including "value of information", "semantic content", and "agency".2Much of our approach can also be used to quantify semantic information in any dynamical system, not just physical systems. For the purposes of this paper, however, we focus our attention on physical systems.

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Section: Nonequilibrium Statistical Physicsmentioning

confidence: 99%

Semantic information, autonomous agency and non-equilibrium statistical physics

2018

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“…In conclusion, based also on our recent findings in quantum computing [36], statistical mechanics [90,91], and information geometry [92,93], we have reason to believe that our information geometric analysis presented in this paper will pave the way to further quantitative investigations on the role played by the Fisher information function in the trade-off between speed and thermodynamic efficiency in quantum search algorithms.…”

Section: Discussionmentioning

confidence: 53%

Decrease of Fisher information and the information geometry of evolution equations for quantum mechanical probability amplitudes

Cafaro¹,

Alsing²

2018

Phys. Rev. E

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The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is characterized by its decrease along the solutions of the Boltzmann equation for Maxwellian molecules in the two-dimensional case. From a quantum mechanical standpoint, the output state in Grover's quantum search algorithm follows a geodesic path obtained from the Fubini-Study metric on the manifold of Hilbert-space rays. Additionally, Grover's algorithm is specified by constant Fisher information. In this paper, we present an information geometric characterization of the oscillatory or monotonic behavior of statistically parametrized squared probability amplitudes originating from special functional forms of the Fisher information function: constant, exponential decay, and power-law decay. Furthermore, for each case, we compute both the computational speed and the availability loss of the corresponding physical processes by exploiting a convenient Riemannian geometrization of useful thermodynamical concepts. Finally, we briefly comment on the possibility of using the proposed methods of information geometry to help identify a suitable trade-off between speed and thermodynamic efficiency in quantum search algorithms.

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“…This result is expected since the information flow increases with the coupling [5,17], therefore it is reasonable to conclude that the larger the coupling is, the smaller the sample size required to infer causality. However, the relationship between N * and η depends on the model.…”

Section: Discussionmentioning

confidence: 88%

“…Transfer Entropy (TE) [1] is an information-theoretical functional able to detect a causal association between two variables [2][3][4][5]. TE identifies the potential driver and driven variable by statistically quantifying the flow of information from one to the other distinguishing the directionality due to its asymmetric property.…”

Section: Introductionmentioning

confidence: 99%

Minimum Sample Size for Reliable Causal Inference Using Transfer Entropy

Ramos

Macau

2017

Entropy

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Transfer Entropy has been applied to experimental datasets to unveil causality between variables. In particular, its application to non-stationary systems has posed a great challenge due to restrictions on the sample size. Here, we have investigated the minimum sample size that produces a reliable causal inference. The methodology has been applied to two prototypical models: the linear model autoregressive-moving average and the non-linear logistic map. The relationship between the Transfer Entropy value and the sample size has been systematically examined. Additionally, we have shown the dependence of the reliable sample size and the strength of coupling between the variables. Our methodology offers a realistic lower bound for the sample size to produce a reliable outcome.

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Thermodynamic aspects of information transfer in complex dynamical systems

Cited by 22 publications

References 33 publications

Semantic information, autonomous agency and non-equilibrium statistical physics

Semantic information, autonomous agency and non-equilibrium statistical physics

Decrease of Fisher information and the information geometry of evolution equations for quantum mechanical probability amplitudes

Minimum Sample Size for Reliable Causal Inference Using Transfer Entropy

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