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Journal of consciousness exploration & research

Entropic Integrated Information Theory: Theory of Consciousness due to Entropy

Siddharth Sharma

Published May 1, 2021• 0 citations
OpenAlex

Abstract

In this paper, I present a mathematical theory of Integrated Information Theory, using entropy as measure of information and hence, as the information distance function. Also, we will consider a set, whose open subsets are mechanisms and topology is the system, we use these two modification in the structure of Integrated Information Theory and Quantum Integrated Information theory, to define Entropic Integrated Information Theory, we will also justify our claims to use why entropy should be use as a measure of cause/effect information and as information distance function using [1]. We will also see the relationship of entanglement with concept and conceptual information. This paper is an attempt to binds consciousness, quantum information, entanglement and quantum mechanics together.

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Entropic Integrated Information Theory-Theory of Consciousness

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In this paper I am going to give a mathematical theory of Integrated Information Theory, using entropy as measure of information and hence, as the information distance function. Also, we will consider a set, whose open subsets are mechanisms and topology is the system, we use these two modification in the structure of Integrated Information Theory [2] and Quantum Integrated Information theory [3], to define Entropic Integrated Information Theory, we will also justify our claims to use why entropy should be use as a measure of cause/effect information and as information distance function using [1]. We will also see the relationship of entanglement with concept and conceptual information. This paper is an attempt to binds consciousness, quantum information, entanglement and quantum mechanics together.

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Integrated Information Theory (IIT) has emerged as one of the leading research lines in computational neuroscience to provide a mechanistic and mathematically well-defined description of the neural correlates of consciousness. Integrated Information ($\Phi$) quantifies how much the integrated cause/effect structure of the global neural network fails to be accounted for by any partitioned version of it. The holistic IIT approach is in principle applicable to any information-processing dynamical network regardless of its interpretation in the context of consciousness. In this paper we take the first steps towards a formulation of a general and consistent version of IIT for interacting networks of quantum systems. A variety of different phases, from the dis-integrated ($\Phi=0$) to the holistic one (extensive $\log\Phi$), can be identified and their cross-overs studied.

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In this paper, I present a mathematical theory of Integrated Information Theory, using entropy as measure of information and hence, as the information distance function. Also, we will consider a set, whose open subsets are mechanisms and topology is the system, we use these two modification in the structure of Integrated Information Theory and Quantum Integrated Information theory, to define Entropic Integrated Information Theory, we will also justify our claims to use why entropy should be use as a measure of cause/effect information and as information distance function using [1]. We will also see the relationship of entanglement with concept and conceptual information. This paper is an attempt to binds consciousness, quantum information, entanglement and quantum mechanics together.
In this paper I am going to give a mathematical theory of Integrated Information Theory, using entropy as measure of information and hence, as the information distance function. Also, we will consider a set, whose open subsets are mechanisms and topology is the system, we use these two modification in the structure of Integrated Information Theory [2] and Quantum Integrated Information theory [3], to define Entropic Integrated Information Theory, we will also justify our claims to use why entropy should be use as a measure of cause/effect information and as information distance function using [1]. We will also see the relationship of entanglement with concept and conceptual information. This paper is an attempt to binds consciousness, quantum information, entanglement and quantum mechanics together.
This paper is an attempt to give a Quantum theory of Mathematical integrated information theory which is mathematical version of integrated information theory by Masafumi Oizumi, Larissa Albantakis, Giulio Tononi [2]. Using the definitions of Classical Mathematical Integrated Information Theory [1]. And considering that the Quantum theory is given by the functor which maps from a category whose objects is topology to a linear category whose objects are Hilbert spaces indexed with the objects from previous category. Also, we will be using the definition of conditional density matrix to define repertoire. We will be also discussing the relationship between consciousness and entanglement.
This paper introduces a novel approach to information theory, leveraging quantum entanglement entropy as a fundamental measure of information. We propose that entanglement entropy can effectively quantify the efficiency of information transmission and provides a theoretical foundation that surpasses the limitations of classical information theory. The core of this work lies in the integration of entanglement entropy with Shannon entropy, establishing a new framework for analyzing information transfer. We explore scenarios where classical information theory struggles to adequately describe the limits of communication due to quantum mechanical effects, specifically entanglement. The paper aims to provide a theoretical underpinning for quantum communication protocols and potentially inform the development of quantum computation. We define key terms and formulate core concepts, focusing on the relationship between entanglement entropy, information content, and the constraints imposed by quantum mechanics. The central argument is that by considering the inherent interconnectedness of entangled systems, we can gain a deeper understanding of information processing at the most fundamental level. ---
Originally conceived as a theory of consciousness, integrated information theory (IIT) provides a theoretical framework intended to characterize the compositional causal information that a system, in its current state, specifies about itself. However, it remains to be determined whether IIT as a theory of consciousness is compatible with quantum mechanics as a theory of microphysics. Here, we present an extension of IIT's latest formalism to evaluate the mechanism integrated information (φ) of a system subset to discrete, finite-dimensional quantum systems (e.g., quantum logic gates). To that end, we translate a recently developed, unique measure of intrinsic information into a density matrix formulation and extend the notion of conditional independence to accommodate quantum entanglement. The compositional nature of the IIT analysis might shed some light on the internal structure of composite quantum states and operators that cannot be obtained using standard information-theoretical analysis. Finally, our results should inform theoretical arguments about the link between consciousness, causation, and physics from the classical to the quantum.
This paper explores the application of entropy dynamics information theory to the description of topological models, specifically incorporating quantum entanglement to investigate potential information transfer and quantum effects within these structures. We propose a novel model centered around the interplay between these two fields, aiming to predict system behavior and evolution paths through a dynamic interplay of information and quantum entanglement. The core mechanism involves constructing a dynamic, quantum-enhanced topological model leveraging the principles of entropy dynamics information theory. This approach offers a framework for understanding the inherent properties of topological systems and potentially uncovering novel quantum phenomena within these models. The research will consider the implications of these predictions on the theoretical understanding of topology and its relationship with quantum mechanics.
Integrated Information Theory (IIT) has emerged as one of the leading research lines in computational neuroscience to provide a mechanistic and mathematically well-defined description of the neural correlates of consciousness. Integrated Information (Φ\PhiΦ) quantifies how much the integrated cause/effect structure of the global neural network fails to be accounted for by any partitioned version of it. The holistic IIT approach is in principle applicable to any information-processing dynamical network regardless of its interpretation in the context of consciousness. In this paper we take the first steps towards a formulation of a general and consistent version of IIT for interacting networks of quantum systems. A variety of different phases, from the dis-integrated (Φ=0\Phi=0Φ=0) to the holistic one (extensive log⁡Φ\log\PhilogΦ), can be identified and their cross-overs studied.