Entropy

32 pages, 1510 KiB

Open AccessArticle

by Hans U. Fuchs, Elisabeth Dumont and Federico Corni

Entropy 2024, 26(12), 1066; https://doi.org/10.3390/e26121066 (registering DOI) - 7 Dec 2024

Carnot treats Heat as a Force of Nature, with its typical fundamental characteristics of intensity and thermal tension (temperature and temperature difference), extension (amount of heat, i.e., caloric), and power. To suggest how the three aspects are related, he applies the imagery of [...] Read more.

Carnot treats Heat as a Force of Nature, with its typical fundamental characteristics of intensity and thermal tension (temperature and temperature difference), extension (amount of heat, i.e., caloric), and power. To suggest how the three aspects are related, he applies the imagery of waterfalls to causative thermal processes: heat powers motion in a heat engine just as falling water does when activating rotation in a water wheel. We understand Carnot’s waterfall imagery as an archetype of human reasoning—as an embodiment of how we experience and understand causative (agentive) phenomena. We project it onto the macroscopic phenomena identified in physical science and so unlock the power of analogical structure mapping between theories of fluids, electricity and magnetism, heat, substances, gravity, and linear and rotational motion. In particular, the notion of (motive) power of a waterfall lets us create imaginative explanations of the interactions of Forces of Nature and helps us construct a generalized energy principle. Two-hundred years after Carnot made us aware of it, his Waterfall Analogy is a powerful example of theory construction with roots deep in how we experience phenomena as caused by natural agents. Full article

(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)

18 pages, 518 KiB

Open AccessArticle

Predictive Complexity of Quantum Subsystems

by Curtis T. Asplund and Elisa Panciu

Entropy 2024, 26(12), 1065; https://doi.org/10.3390/e26121065 (registering DOI) - 7 Dec 2024

Abstract

We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of predictive state analysis of stochastic and complex systems theory but is [...] Read more.

We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of predictive state analysis of stochastic and complex systems theory but is intrinsically quantum. Predictive states of a subsystem are formed by equivalence classes of state vectors in the exterior Hilbert space that effectively predict the same future behavior of that subsystem for some time. As an illustrative example, we present calculations in the dynamics of an isotropic Heisenberg model spin chain and show that, in comparison to the entanglement entropy, the predictive complexity better signifies dynamically important events, such as magnon collisions. It can also serve as a local order parameter that can distinguish long and short range entanglement. Full article

(This article belongs to the Section Quantum Information)

11 pages, 283 KiB

Open AccessArticle

Entropic Order Parameters for Categorical Symmetries in 2D-CFT

by Javier Molina-Vilaplana, Pablo Saura-Bastida and Germán Sierra

Entropy 2024, 26(12), 1064; https://doi.org/10.3390/e26121064 - 6 Dec 2024

Abstract

In this work, we propose an information theoretic order parameter able to characterize the presence and breaking of categorical symmetries in

(1 + 1)

-d rational conformal field theories (RCFTs). Specifically, we compute the quantum relative entropy between the ground states [...] Read more.

In this work, we propose an information theoretic order parameter able to characterize the presence and breaking of categorical symmetries in

(1 + 1)

-d rational conformal field theories (RCFTs). Specifically, we compute the quantum relative entropy between the ground states of RCFTs representing the critical point of phase transitions between different symmetry-broken phases of theories with categorical symmetries, and their symmetrized versions. We find that, at leading order in the high temperature limit, this relative entropy only depends on the expectation values of the quantum dimensions of the topological operators implementing the categorical symmetry. This dependence suggests that our proposal can be used to characterize the different broken phases of

(1 + 1)

-d theories with categorical symmetries. Full article

(This article belongs to the Special Issue Entanglement Entropy in Quantum Field Theory)

22 pages, 3660 KiB

Open AccessArticle

Robust Model-Free Identification of the Causal Networks Underlying Complex Nonlinear Systems

by Guanxue Yang, Shimin Lei and Guanxiao Yang

Entropy 2024, 26(12), 1063; https://doi.org/10.3390/e26121063 - 6 Dec 2024

Abstract

Inferring causal networks from noisy observations is of vital importance in various fields. Due to the complexity of system modeling, the way in which universal and feasible inference algorithms are studied is a key challenge for network reconstruction. In this study, without any [...] Read more.

Inferring causal networks from noisy observations is of vital importance in various fields. Due to the complexity of system modeling, the way in which universal and feasible inference algorithms are studied is a key challenge for network reconstruction. In this study, without any assumptions, we develop a novel model-free framework to uncover only the direct relationships in networked systems from observations of their nonlinear dynamics. Our proposed methods are termed multiple-order Polynomial Conditional Granger Causality (PCGC) and sparse PCGC (SPCGC). PCGC mainly adopts polynomial functions to approximate the whole system model, which can be used to judge the interactions among nodes through subsequent nonlinear Granger causality analysis. For SPCGC, Lasso optimization is first used for dimension reduction, and then PCGC is executed to obtain the final network. Specifically, the conditional variables are fused in this general, model-free framework regardless of their formulations in the system model, which could effectively reconcile the inference of direct interactions with an indirect influence. Based on many classical dynamical systems, the performances of PCGC and SPCGC are analyzed and verified. Generally, the proposed framework could be quite promising for the provision of certain guidance for data-driven modeling with an unknown model. Full article

(This article belongs to the Special Issue Causality and Complex Systems)

20 pages, 4184 KiB

Open AccessArticle

Air Quality Prediction Based on Singular Spectrum Analysis and Artificial Neural Networks

by Javier Linkolk López-Gonzales, Rodrigo Salas, Daira Velandia and Paulo Canas Rodrigues

Entropy 2024, 26(12), 1062; https://doi.org/10.3390/e26121062 - 6 Dec 2024

Abstract

Singular spectrum analysis is a powerful nonparametric technique used to decompose the original time series into a set of components that can be interpreted as trend, seasonal, and noise. For their part, neural networks are a family of information-processing techniques capable of approximating [...] Read more.

Singular spectrum analysis is a powerful nonparametric technique used to decompose the original time series into a set of components that can be interpreted as trend, seasonal, and noise. For their part, neural networks are a family of information-processing techniques capable of approximating highly nonlinear functions. This study proposes to improve the precision in the prediction of air quality. For this purpose, a hybrid adaptation is considered. It is based on an integration of the singular spectrum analysis and the recurrent neural network long short-term memory; the SSA is applied to the original time series to split signal and noise, which are then predicted separately and added together to obtain the final forecasts. This hybrid method provided better performance when compared with other methods. Full article

(This article belongs to the Special Issue Big Data Analytics and Information Science for Business and Biomedical Applications: Third Edition)

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27 pages, 428 KiB

Open AccessArticle

Identifying Causal Effects Under Functional Dependencies

by Yizuo Chen and Adnan Darwiche

Entropy 2024, 26(12), 1061; https://doi.org/10.3390/e26121061 - 6 Dec 2024

Abstract

We study the identification of causal effects, motivated by two improvements to identifiability that can be attained if one knows that some variables in a causal graph are functionally determined by their parents (without needing to know the specific functions). First, an unidentifiable [...] Read more.

We study the identification of causal effects, motivated by two improvements to identifiability that can be attained if one knows that some variables in a causal graph are functionally determined by their parents (without needing to know the specific functions). First, an unidentifiable causal effect may become identifiable when certain variables are functional. Secondly, certain functional variables can be excluded from being observed without affecting the identifiability of a causal effect, which may significantly reduce the number of needed variables in observational data. Our results are largely based on an elimination procedure that removes functional variables from a causal graph while preserving key properties in the resulting causal graph, including the identifiability of causal effects. Our treatment of functional dependencies in this context mandates a formal, systematic, and general treatment of positivity assumptions, which are prevalent in the literature on causal effect identifiability and which interact with functional dependencies, leading to another contribution of the presented work. Full article

(This article belongs to the Special Issue Causal Graphical Models and Their Applications)

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11 pages, 1800 KiB

Open AccessArticle

Interplay of Spin Nernst Effect and Entanglement Negativity in Layered Ferrimagnets: A Study via Exact Diagonalization

by Leonardo S. Lima

Entropy 2024, 26(12), 1060; https://doi.org/10.3390/e26121060 - 6 Dec 2024

Abstract

In this paper, we analyzed the influence of the spin Nernst effect on quantum correlation in a layered ferrimagnetic model. In the study of three-dimensional ferrimagnets, the focus is on materials with a specific arrangement of spins, where the neighboring spins are parallel [...] Read more.

In this paper, we analyzed the influence of the spin Nernst effect on quantum correlation in a layered ferrimagnetic model. In the study of three-dimensional ferrimagnets, the focus is on materials with a specific arrangement of spins, where the neighboring spins are parallel and the others are antiparallel. The anisotropic nature of these materials means that the interactions between spins depend on their relative orientations in different directions. We analyzed the effect of magnon bands induced by the coupling parameters on entanglement negativity. The influence of the coupling parameters of the topologic phase transition on quantum entanglement is investigated as well. Numerical simulations using the Lanczos algorithm and exact diagonalization for different lattice sizes are compared with the results of spin wave theory. Full article

(This article belongs to the Special Issue Entanglement in Quantum Spin Systems)

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19 pages, 7347 KiB

Open AccessArticle

Adapting SAM2 Model from Natural Images for Tooth Segmentation in Dental Panoramic X-Ray Images

by Zifeng Li, Wenzhong Tang, Shijun Gao, Yanyang Wang and Shuai Wang

Entropy 2024, 26(12), 1059; https://doi.org/10.3390/e26121059 - 6 Dec 2024

Abstract

Dental panoramic X-ray imaging, due to its high cost-effectiveness and low radiation dose, has become a widely used diagnostic tool in dentistry. Accurate tooth segmentation is crucial for lesion analysis and treatment planning, helping dentists to quickly and precisely assess the condition of [...] Read more.

Dental panoramic X-ray imaging, due to its high cost-effectiveness and low radiation dose, has become a widely used diagnostic tool in dentistry. Accurate tooth segmentation is crucial for lesion analysis and treatment planning, helping dentists to quickly and precisely assess the condition of teeth. However, dental X-ray images often suffer from noise, low contrast, and overlapping anatomical structures, coupled with limited available datasets, leading traditional deep learning models to experience overfitting, which affects generalization ability. In addition, high-precision deep models typically require significant computational resources for inference, making deployment in real-world applications challenging. To address these challenges, this paper proposes a tooth segmentation method based on the pre-trained SAM2 model. We employ adapter modules to fine-tune the SAM2 model and introduce ScConv modules and gated attention mechanisms to enhance the model’s semantic understanding and multi-scale feature extraction capabilities for medical images. In terms of efficiency, we utilize knowledge distillation, using the fine-tuned SAM2 model as the teacher model for distilling knowledge to a smaller model named LightUNet. Experimental results on the UFBA-UESC dataset show that, in terms of performance, our model significantly outperforms the traditional UNet model in multiple metrics such as IoU, effectively improving segmentation accuracy and model robustness, particularly with limited sample datasets. In terms of efficiency, LightUNet achieves comparable performance to UNet, but with only 1.6% of its parameters and 24.0% of the inference time, demonstrating its feasibility for deployment on edge devices. Full article

(This article belongs to the Section Multidisciplinary Applications)

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19 pages, 1210 KiB

Open AccessArticle

Contraction Heuristics for Tensor Decision Diagrams

by Christian Bøgh Larsen, Simon Brun Olsen, Kim Guldstrand Larsen and Christian Schilling

Entropy 2024, 26(12), 1058; https://doi.org/10.3390/e26121058 - 5 Dec 2024

Abstract

In this paper, we study the equivalence problem for quantum circuits: Given two quantum circuits, are they equivalent? We reduce this problem to the contraction problem of a tensor network. The order in which the contraction operations between tensors are applied has a [...] Read more.

In this paper, we study the equivalence problem for quantum circuits: Given two quantum circuits, are they equivalent? We reduce this problem to the contraction problem of a tensor network. The order in which the contraction operations between tensors are applied has a crucial impact on efficiency, which is why many heuristics have been proposed. In this work, we use an efficient representation of tensors as a tensor decision diagram. Since existing contraction heuristics do not perform well in combination with these diagrams, we propose two new contraction heuristics. We demonstrate experimentally that our heuristics outperform other state-of-the-art heuristics. We also demonstrate that our framework yields state-of-the-art performance for equivalence checking. Full article

(This article belongs to the Special Issue Quantum Computing in the NISQ Era)

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20 pages, 495 KiB

Open AccessArticle

Solving the Independent Domination Problem by the Quantum Approximate Optimization Algorithm

by Haoqian Pan and Changhong Lu

Entropy 2024, 26(12), 1057; https://doi.org/10.3390/e26121057 - 5 Dec 2024

Abstract

In the wake of quantum computing advancements and quantum algorithmic progress, quantum algorithms are increasingly being employed to address a myriad of combinatorial optimization problems. Among these, the Independent Domination Problem (IDP), a derivative of the Domination Problem, has practical implications in various [...] Read more.

In the wake of quantum computing advancements and quantum algorithmic progress, quantum algorithms are increasingly being employed to address a myriad of combinatorial optimization problems. Among these, the Independent Domination Problem (IDP), a derivative of the Domination Problem, has practical implications in various real-world scenarios. Despite this, existing classical algorithms for the IDP are plagued by high computational complexity, and quantum algorithms have yet to tackle this challenge. This paper introduces a Quantum Approximate Optimization Algorithm (QAOA)-based approach to address the IDP. Utilizing IBM’s qasm_simulator, we have demonstrated the efficacy of the QAOA in solving the IDP under specific parameter settings, with a computational complexity that surpasses that of classical methods. Our findings offer a novel avenue for the resolution of the IDP. Full article

(This article belongs to the Special Issue Quantum Computing in the NISQ Era)

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15 pages, 5604 KiB

Open AccessArticle

A Deep Evolution Policy-Based Approach for RIS-Enhanced Communication System

by Ke Zhao, Zhiqun Song, Yong Li, Xingjian Li, Lizhe Liu and Bin Wang

Entropy 2024, 26(12), 1056; https://doi.org/10.3390/e26121056 - 5 Dec 2024

Abstract

This paper investigates the design of active and passive beamforming in a reconfigurable intelligent surface (RIS)-aided multi-user multiple-input single-output (MU-MISO) system with the objective of maximizing the sum rate. We propose a deep evolution policy (DEP)-based algorithm to derive the optimal beamforming strategy [...] Read more.

This paper investigates the design of active and passive beamforming in a reconfigurable intelligent surface (RIS)-aided multi-user multiple-input single-output (MU-MISO) system with the objective of maximizing the sum rate. We propose a deep evolution policy (DEP)-based algorithm to derive the optimal beamforming strategy by generating multiple agents, each utilizing distinct deep neural networks (DNNs). Additionally, a random subspace selection (RSS) strategy is incorporated to effectively balance exploitation and exploration. The proposed DEP-based algorithm operates without the need for alternating iterations, gradient descent, or backpropagation, enabling simultaneous optimization of both active and passive beamforming. Simulation results indicate that the proposed algorithm can bring significant performance enhancements. Full article

(This article belongs to the Special Issue Information Theory in Emerging Wireless Communication Systems and Networks, Second Edition)

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13 pages, 423 KiB

Open AccessArticle

Joint User Association, Power Allocation and Beamforming for NOMA-Based Integrated Satellite–Terrestrial Networks

by Peizhe Xin, Zihao Fu, Zhiyi Chen, Jing Jiang, Jing Zou, Yu Zhang and Xinyue Hu

Entropy 2024, 26(12), 1055; https://doi.org/10.3390/e26121055 - 5 Dec 2024

Abstract

This paper investigated a non-orthogonal multiple access (NOMA)-based integrated satellite–terrestrial network (ISTN), where each user can select to access a terrestrial base station (BS) or the satellite according to the capacity of BS and their individual transmission requirements. A two-stage algorithm is proposed [...] Read more.

This paper investigated a non-orthogonal multiple access (NOMA)-based integrated satellite–terrestrial network (ISTN), where each user can select to access a terrestrial base station (BS) or the satellite according to the capacity of BS and their individual transmission requirements. A two-stage algorithm is proposed to solve the achievable sum rate maximizing resource optimization problem. In the first stage, user associations are determined based on individual preference lists and the backhaul capacities of the access points (APs). In the second stage, the power allocation, and the receiving beamforming vectors are optimized alternately. Within each iteration, the closed-form solution for the transmit power is derived. Simulation results show the effectiveness of the proposed algorithm and the benefits brought by NOMA. When the backhaul link capacity of terrestrial BSs is sufficient, users (UEs) prefer to access these BSs. Otherwise, the satellite can offer QoS guarantees to UEs. Furthermore, the overall system performance reaches its optimum when the number of UEs in the system matches the number of receive antennas at the APs. Full article

(This article belongs to the Special Issue Advanced New Physical Layer Technologies for Next-Generation Wireless Communications)

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20 pages, 845 KiB

Open AccessFeature PaperArticle

Kinetic Theory of Self-Propelled Particles with Nematic Alignment

by Horst-Holger Boltz, Benjamin Kohler and Thomas Ihle

Entropy 2024, 26(12), 1054; https://doi.org/10.3390/e26121054 - 4 Dec 2024

Abstract

We present the results from kinetic theory for a system of self-propelled particles with alignment interactions of higher-order symmetry, particularly nematic ones. To this end, we use the Landau equation approach, a systematic approximation to the BBGKY hierarchy for small effective couplings. Our [...] Read more.

We present the results from kinetic theory for a system of self-propelled particles with alignment interactions of higher-order symmetry, particularly nematic ones. To this end, we use the Landau equation approach, a systematic approximation to the BBGKY hierarchy for small effective couplings. Our calculations are presented in a pedagogical way with the explicit goal of serving as a tutorial from a physicists’ perspective into applying kinetic theory ideas beyond mean-field to active matter systems with essentially no prerequisites and yield predictions without free parameters that are in quantitative agreement with direct agent-based simulations Full article

(This article belongs to the Collection Foundations of Statistical Mechanics)

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33 pages, 855 KiB

Open AccessArticle

Statistical Testing of Random Number Generators and Their Improvement Using Randomness Extraction

by Cameron Foreman, Richie Yeung and Florian J. Curchod

Entropy 2024, 26(12), 1053; https://doi.org/10.3390/e26121053 - 4 Dec 2024

Abstract

Random number generators (RNGs) are notoriously challenging to build and test, especially for cryptographic applications. While statistical tests cannot definitively guarantee an RNG’s output quality, they are a powerful verification tool and the only universally applicable testing method. In this work, we design, [...] Read more.

Random number generators (RNGs) are notoriously challenging to build and test, especially for cryptographic applications. While statistical tests cannot definitively guarantee an RNG’s output quality, they are a powerful verification tool and the only universally applicable testing method. In this work, we design, implement, and present various post-processing methods, using randomness extractors, to improve the RNG output quality and compare them through statistical testing. We begin by performing intensive tests on three RNGs—the 32-bit linear feedback shift register (LFSR), Intel’s ‘RDSEED,’ and IDQuantique’s ‘Quantis’—and compare their performance. Next, we apply the different post-processing methods to each RNG and conduct further intensive testing on the processed output. To facilitate this, we introduce a comprehensive statistical testing environment, based on existing test suites, that can be parametrised for lightweight (fast) to intensive testing. Full article

(This article belongs to the Special Issue Quantum Probability and Randomness V)

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14 pages, 10265 KiB

Open AccessArticle

Performance Analysis of Troposphere Scattering Communication Channel with Chirp-BOK Modulation

by Junhu Shao, Zaiping Liu, Yishuo Liu and Tianjiao Xie

Entropy 2024, 26(12), 1052; https://doi.org/10.3390/e26121052 - 4 Dec 2024

Abstract

By utilizing chirp-BOK (binary orthogonal keying) modulation into a troposphere scattering communication system, a lower demodulation threshold can be achieved with excellent linear frequency modulation properties in a strong noise and weak signal environment. Firstly, the bit error rate (BER) formula of chirp-BOK [...] Read more.

By utilizing chirp-BOK (binary orthogonal keying) modulation into a troposphere scattering communication system, a lower demodulation threshold can be achieved with excellent linear frequency modulation properties in a strong noise and weak signal environment. Firstly, the bit error rate (BER) formula of chirp-BOK modulation over a Rayleigh fading channel was derived theoretically. Then, the BER performance with different chirp-BOK parameters were numerically calculated. In order to investigate the performance of chirp-BOK over deeping fading troposphere scattering link, a seven-path equal-delay Rayleigh fading model was employed. Finally, the system BER performance was simulated under different tap delay and time–bandwidth product parameters. The results demonstrate that when BER reaches

10^{- 4}

, the optimal configuration of the system achieves a gains approximately from 1.7 dB to 10 dB compared to non-optimized configuration under different Path-Gain-Vector with varying tap delays. Full article

(This article belongs to the Special Issue Advanced New Physical Layer Technologies for Next-Generation Wireless Communications)

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17 pages, 327 KiB

Open AccessArticle

An Intrinsic Characterization of Shannon’s and Rényi’s Entropy

by Martin Schlather and Carmen Ditscheid

Entropy 2024, 26(12), 1051; https://doi.org/10.3390/e26121051 - 4 Dec 2024

Abstract

All characterizations of the Shannon entropy include the so-called chain rule, a formula on a hierarchically structured probability distribution, which is based on at least two elementary distributions. We show that the chain rule can be split into two natural components, the well-known [...] Read more.

All characterizations of the Shannon entropy include the so-called chain rule, a formula on a hierarchically structured probability distribution, which is based on at least two elementary distributions. We show that the chain rule can be split into two natural components, the well-known additivity of the entropy in case of cross-products and a variant of the chain rule that involves only a single elementary distribution. The latter is given as a proportionality relation and, hence, allows a vague interpretation as self-similarity, hence intrinsic property of the Shannon entropy. Analogous characterizations are given for the Rényi entropy and its limits, the min-entropy and the Hartley entropy. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

22 pages, 1690 KiB

Open AccessArticle

Cascades Towards Noise-Induced Transitions on Networks Revealed Using Information Flows

by Casper van Elteren, Rick Quax and Peter M. A. Sloot

Entropy 2024, 26(12), 1050; https://doi.org/10.3390/e26121050 - 4 Dec 2024

Abstract

Complex networks, from neuronal assemblies to social systems, can exhibit abrupt, system-wide transitions without external forcing. These endogenously generated “noise-induced transitions” emerge from the intricate interplay between network structure and local dynamics, yet their underlying mechanisms remain elusive. Our study unveils two critical [...] Read more.

Complex networks, from neuronal assemblies to social systems, can exhibit abrupt, system-wide transitions without external forcing. These endogenously generated “noise-induced transitions” emerge from the intricate interplay between network structure and local dynamics, yet their underlying mechanisms remain elusive. Our study unveils two critical roles that nodes play in catalyzing these transitions within dynamical networks governed by the Boltzmann–Gibbs distribution. We introduce the concept of “initiator nodes”, which absorb and propagate short-lived fluctuations, temporarily destabilizing their neighbors. This process initiates a domino effect, where the stability of a node inversely correlates with the number of destabilized neighbors required to tip it. As the system approaches a tipping point, we identify “stabilizer nodes” that encode the system’s long-term memory, ultimately reversing the domino effect and settling the network into a new stable attractor. Through targeted interventions, we demonstrate how these roles can be manipulated to either promote or inhibit systemic transitions. Our findings provide a novel framework for understanding and potentially controlling endogenously generated metastable behavior in complex networks. This approach opens new avenues for predicting and managing critical transitions in diverse fields, from neuroscience to social dynamics and beyond. Full article

(This article belongs to the Special Issue 180th Anniversary of Ludwig Boltzmann)

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21 pages, 7739 KiB

Open AccessArticle

On the Capacity of the Peak-Limited and Band-Limited Channel

by Michael Peleg and Shlomo Shamai

Entropy 2024, 26(12), 1049; https://doi.org/10.3390/e26121049 - 3 Dec 2024

Abstract

We investigate the peak-power limited (PPL) Additive White Gaussian Noise (AWGN) channels in which the signal is band-limited, and its instantaneous power cannot exceed the power P. This model is relevant to many communication systems; however, its capacity is still unknown. We [...] Read more.

We investigate the peak-power limited (PPL) Additive White Gaussian Noise (AWGN) channels in which the signal is band-limited, and its instantaneous power cannot exceed the power P. This model is relevant to many communication systems; however, its capacity is still unknown. We use a new geometry-based approach which evaluates the maximal entropy of the transmitted signal by assessing the volume of the body, in the space of Nyquist-rate samples, comprising all the points the transmitted signal can reach. This leads to lower bounds on capacity which are tight at high Signal to Noise Ratios (SNRs). We find lower bounds on capacity, expressed as power efficiency, that were higher than the known ones by a factor of 3.3 and 8.6 in the low-pass and the band-pass cases, respectively. The gap to the upper bounds is reduced to a power ratio of 1.5. The new bounds are numerically evaluated for FDMA-style signals with limited duration and also are derived in the general case as a conjecture. The penalty in power efficiency due to the peak power constraint is roughly 6 dB at high SNRs. Further research is needed to develop effective modulation and coding for this channel. Full article

(This article belongs to the Special Issue Advanced New Physical Layer Technologies for Next-Generation Wireless Communications)

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12 pages, 4313 KiB

Open AccessCommunication

Metastable Oscillatory Modes as a Signature of Entropy Management in the Brain

by Marta Xavier, Patrícia Figueiredo, Gustavo Deco, Andrea I. Luppi and Joana Cabral

Entropy 2024, 26(12), 1048; https://doi.org/10.3390/e26121048 - 3 Dec 2024

Abstract

Entropy management, central to the Free Energy Principle, requires a process that temporarily shifts brain activity toward states of lower or higher entropy. Metastable synchronization is a process by which a system achieves entropy fluctuations by intermittently transitioning between states of collective order [...] Read more.

Entropy management, central to the Free Energy Principle, requires a process that temporarily shifts brain activity toward states of lower or higher entropy. Metastable synchronization is a process by which a system achieves entropy fluctuations by intermittently transitioning between states of collective order and disorder. Previous work has shown that collective oscillations, similar to those recorded from the brain, emerge spontaneously from weakly stable synchronization in critically coupled oscillator systems. However, direct evidence linking the formation of collective oscillations to entropy fluctuations is lacking. In this short communication, we demonstrate how the emergence of Metastable Oscillatory Modes (MOMs) is directly associated with a temporary reduction in entropy in the ongoing dynamics. We apply Shannon entropy to the distribution of eigenvalues of phase covariance over sliding time windows, capturing the temporal evolution of entropy at the level of the entire dynamical system. By demonstrating how the formation of MOMs impacts a system’s entropy levels, we bridge theoretical works on the physics of coupled oscillators with the FEP framework, supporting the hypothesis that brain rhythms recorded experimentally are a signature of entropy management. Full article

(This article belongs to the Special Issue From Functional Imaging to Free Energy—Dedicated to Professor Karl Friston on the Occasion of His 65th Birthday)

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