Entropy

37 pages, 1782 KiB

Open AccessArticle

Contrast Information Dynamics: A Novel Information Measure for Cognitive Modelling

by Steven T. Homer, Nicholas Harley and Geraint A. Wiggins

Entropy 2024, 26(8), 638; https://doi.org/10.3390/e26080638 (registering DOI) - 27 Jul 2024

We present contrast information, a novel application of some specific cases of relative entropy, designed to be useful for the cognitive modelling of the sequential perception of continuous signals. We explain the relevance of entropy in the cognitive modelling of sequential phenomena [...] Read more.

We present contrast information, a novel application of some specific cases of relative entropy, designed to be useful for the cognitive modelling of the sequential perception of continuous signals. We explain the relevance of entropy in the cognitive modelling of sequential phenomena such as music and language. Then, as a first step to demonstrating the utility of constrast information for this purpose, we empirically show that its discrete case correlates well with existing successful cognitive models in the literature. We explain some interesting properties of constrast information. Finally, we propose future work toward a cognitive architecture that uses it. Full article

(This article belongs to the Collection Feature Papers in Information Theory)

23 pages, 7834 KiB

Open AccessFeature PaperArticle

Understanding Higher-Order Interactions in Information Space

by Herbert Edelsbrunner, Katharina Ölsböck and Hubert Wagner

Entropy 2024, 26(8), 637; https://doi.org/10.3390/e26080637 (registering DOI) - 27 Jul 2024

Abstract

Methods used in topological data analysis naturally capture higher-order interactions in point cloud data embedded in a metric space. This methodology was recently extended to data living in an information space, by which we mean a space measured with an information theoretical distance. [...] Read more.

Methods used in topological data analysis naturally capture higher-order interactions in point cloud data embedded in a metric space. This methodology was recently extended to data living in an information space, by which we mean a space measured with an information theoretical distance. One such setting is a finite collection of discrete probability distributions embedded in the probability simplex measured with the relative entropy (Kullback–Leibler divergence). More generally, one can work with a Bregman divergence parameterized by a different notion of entropy. While theoretical algorithms exist for this setup, there is a paucity of implementations for exploring and comparing geometric-topological properties of various information spaces. The interest of this work is therefore twofold. First, we propose the first robust algorithms and software for geometric and topological data analysis in information space. Perhaps surprisingly, despite working with Bregman divergences, our design reuses robust libraries for the Euclidean case. Second, using the new software, we take the first steps towards understanding the geometric-topological structure of these spaces. In particular, we compare them with the more familiar spaces equipped with the Euclidean and Fisher metrics. Full article

(This article belongs to the Special Issue Topological Data Analysis Meets Information Theory. New Perspectives for the Analysis of Higher-Order Interactions in Complex Systems)

10 pages, 357 KiB

Open AccessArticle

Kramers–Wannier Duality and Random-Bond Ising Model

by Chaoming Song

Entropy 2024, 26(8), 636; https://doi.org/10.3390/e26080636 (registering DOI) - 27 Jul 2024

Abstract

We present a new combinatorial approach to the Ising model incorporating arbitrary bond weights on planar graphs. In contrast to existing methodologies, the exact free energy is expressed as the determinant of a set of ordered and disordered operators defined on a planar [...] Read more.

We present a new combinatorial approach to the Ising model incorporating arbitrary bond weights on planar graphs. In contrast to existing methodologies, the exact free energy is expressed as the determinant of a set of ordered and disordered operators defined on a planar graph and the corresponding dual graph, respectively, thereby explicitly demonstrating the Kramers–Wannier duality. The implications of our derived formula for the Random-Bond Ising Model are further elucidated. Full article

(This article belongs to the Special Issue A Journey Through Complex Landscapes—Dedicated to Professor Giorgio Parisi to Celebrate the Nobel Prize & His 75th Birthday)

14 pages, 6349 KiB

Open AccessArticle

Practical Performance Analysis of MDI-QKD with Orbital Angular Momentum on UAV Relay Platform

by Dan Wu, Jiahao Li, Lan Yang, Zhifeng Deng, Jie Tang, Yuexiang Cao, Ying Liu, Haoran Hu, Ya Wang, Huicun Yu, Jiahua Wei, Huazhi Lun, Xingyu Wang and Lei Shi

Entropy 2024, 26(8), 635; https://doi.org/10.3390/e26080635 (registering DOI) - 27 Jul 2024

Abstract

The integration of terrestrial- and satellite-based quantum key distribution (QKD) experiments has markedly advanced global-scale quantum networks, showcasing the growing maturity of quantum technologies. Notably, the use of unmanned aerial vehicles (UAVs) as relay nodes has emerged as a promising method to overcome [...] Read more.

The integration of terrestrial- and satellite-based quantum key distribution (QKD) experiments has markedly advanced global-scale quantum networks, showcasing the growing maturity of quantum technologies. Notably, the use of unmanned aerial vehicles (UAVs) as relay nodes has emerged as a promising method to overcome the inherent limitations of fiber-based and low-Earth orbit (LEO) satellite connections. This paper introduces a protocol for measurement-device-independent QKD (MDI-QKD) using photon orbital angular momentum (OAM) encoding, with UAVs as relay platforms. Leveraging UAV mobility, the protocol establishes a secure and efficient link, mitigating threats from untrusted UAVs. Photon OAM encoding addresses reference frame alignment issues exacerbated by UAV jitter. A comprehensive analysis of atmospheric turbulence, state-dependent diffraction (SDD), weather visibility, and pointing errors on free-space OAM-state transmission systems was conducted. This analysis elucidates the relationship between the key generation rate and propagation distance for the proposed protocol. Results indicate that considering SDD significantly decreases the key rate, halving previous data results. Furthermore, the study identifies a maximum channel loss capacity of 26 dB for the UAV relay platform.This result is pivotal in setting realistic parameters for the deployment of UAV-based quantum communications and lays the foundation for practical implementation strategies in the field. Full article

(This article belongs to the Special Issue Progress in Quantum Key Distribution)

52 pages, 6865 KiB

Open AccessReview

The Road to Safety: A Review of Uncertainty and Applications to Autonomous Driving Perception

by Bernardo Araújo, João F. Teixeira, Joaquim Fonseca, Ricardo Cerqueira and Sofia C. Beco

Entropy 2024, 26(8), 634; https://doi.org/10.3390/e26080634 - 26 Jul 2024

Abstract

Deep learning approaches have been gaining importance in several applications. However, the widespread use of these methods in safety-critical domains, such as Autonomous Driving, is still dependent on their reliability and trustworthiness. The goal of this paper is to provide a review of [...] Read more.

Deep learning approaches have been gaining importance in several applications. However, the widespread use of these methods in safety-critical domains, such as Autonomous Driving, is still dependent on their reliability and trustworthiness. The goal of this paper is to provide a review of deep learning-based uncertainty methods and their applications to support perception tasks for Autonomous Driving. We detail significant Uncertainty Quantification and calibration methods, and their contributions and limitations, as well as important metrics and concepts. We present an overview of the state of the art of out-of-distribution detection and active learning, where uncertainty estimates are commonly applied. We show how these methods have been applied in the automotive context, providing a comprehensive analysis of reliable AI for Autonomous Driving. Finally, challenges and opportunities for future work are discussed for each topic. Full article

(This article belongs to the Section Entropy Reviews)

11 pages, 257 KiB

Open AccessArticle

Optimized Tail Bounds for Random Matrix Series

by Xianjie Gao, Mingliang Zhang and Jinming Luo

Entropy 2024, 26(8), 633; https://doi.org/10.3390/e26080633 - 26 Jul 2024

Abstract

Random matrix series are a significant component of random matrix theory, offering rich theoretical content and broad application prospects. In this paper, we propose modified versions of tail bounds for random matrix series, including matrix Gaussian (or Rademacher) and sub-Gaussian and infinitely divisible [...] Read more.

Random matrix series are a significant component of random matrix theory, offering rich theoretical content and broad application prospects. In this paper, we propose modified versions of tail bounds for random matrix series, including matrix Gaussian (or Rademacher) and sub-Gaussian and infinitely divisible (i.d.) series. Unlike present studies, our results depend on the intrinsic dimension instead of ambient dimension. In some cases, the intrinsic dimension is much smaller than ambient dimension, which makes the modified versions suitable for high-dimensional or infinite-dimensional setting possible. In addition, we obtain the expectation bounds for random matrix series based on the intrinsic dimension. Full article

(This article belongs to the Special Issue Random Matrix Theory and Its Innovative Applications)

25 pages, 2010 KiB

Open AccessArticle

Congestion Transition on Random Walks on Graphs

by Lorenzo Di Meco, Mirko Degli Esposti, Federico Bellisardi and Armando Bazzani

Entropy 2024, 26(8), 632; https://doi.org/10.3390/e26080632 - 26 Jul 2024

Abstract

The formation of congestion on an urban road network is a key issue for the development of sustainable mobility in future smart cities. In this work, we propose a reductionist approach by studying the stationary states of a simple transport model using a [...] Read more.

The formation of congestion on an urban road network is a key issue for the development of sustainable mobility in future smart cities. In this work, we propose a reductionist approach by studying the stationary states of a simple transport model using a random process on a graph, where each node represents a location and the link weights give the transition rates to move from one node to another, representing the mobility demand. Each node has a maximum flow rate and a maximum load capacity, and we assume that the average incoming flow equals the outgoing flow. In the approximation of the single-step process, we are able to analytically characterize the traffic load distribution on the single nodes using a local maximum entropy principle. Our results explain how congested nodes emerge as the total traffic load increases, analogous to a percolation transition where the appearance of a congested node is an independent random event. However, using numerical simulations, we show that in the more realistic case of synchronous dynamics for the nodes, entropic forces introduce correlations among the node states and favor the clustering of empty and congested nodes. Our aim is to highlight the universal properties of congestion formation and, in particular, to understand the role of traffic load fluctuations as a possible precursor of congestion in a transport network. Full article

(This article belongs to the Special Issue Random Walks and Stochastic Processes in Complex Systems: From Physics to Socio-Economic Phenomena)

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10 pages, 3626 KiB

Open AccessArticle

Evolution of Telencephalon Anterior–Posterior Patterning through Core Endogenous Network Bifurcation

by Chen Sun, Mengchao Yao, Ruiqi Xiong, Yang Su, Binglin Zhu, Yong-Cong Chen and Ping Ao

Entropy 2024, 26(8), 631; https://doi.org/10.3390/e26080631 - 26 Jul 2024

Abstract

How did the complex structure of the telencephalon evolve? Existing explanations are based on phenomena and lack a first-principles account. The Darwinian dynamics and endogenous network theory—established decades ago—provides a mathematical and theoretical framework and a general constitutive structure for theory–experiment coupling for [...] Read more.

How did the complex structure of the telencephalon evolve? Existing explanations are based on phenomena and lack a first-principles account. The Darwinian dynamics and endogenous network theory—established decades ago—provides a mathematical and theoretical framework and a general constitutive structure for theory–experiment coupling for answering this question from a first-principles perspective. By revisiting a gene network that explains the anterior–posterior patterning of the vertebrate telencephalon, we found that upon increasing the cooperative effect within this network, fixed points gradually evolve, accompanied by the occurrence of two bifurcations. The dynamic behavior of this network is informed by the knowledge obtained from experiments on telencephalic evolution. Our work provides a quantitative explanation for how telencephalon anterior–posterior patterning evolved from the pre-vertebrate chordate to the vertebrate and provides a series of verifiable predictions from a first-principles perspective. 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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12 pages, 1877 KiB

Open AccessArticle

Breast Cancer Detection with Quanvolutional Neural Networks

by Nadine Matondo-Mvula and Khaled Elleithy

Entropy 2024, 26(8), 630; https://doi.org/10.3390/e26080630 - 26 Jul 2024

Abstract

Quantum machine learning holds the potential to revolutionize cancer treatment and diagnostic imaging by uncovering complex patterns beyond the reach of classical methods. This study explores the effectiveness of quantum convolutional layers in classifying ultrasound breast images for cancer detection. By encoding classical [...] Read more.

Quantum machine learning holds the potential to revolutionize cancer treatment and diagnostic imaging by uncovering complex patterns beyond the reach of classical methods. This study explores the effectiveness of quantum convolutional layers in classifying ultrasound breast images for cancer detection. By encoding classical data into quantum states through angle embedding and employing a robustly entangled 9-qubit circuit design with an SU(4) gate, we developed a Quantum Convolutional Neural Network (QCNN) and compared it to a classical CNN of similar architecture. Our QCNN model, leveraging two quantum circuits as convolutional layers, achieved an impressive peak training accuracy of 76.66% and a validation accuracy of 87.17% at a learning rate of 1 × 10⁻². In contrast, the classical CNN model attained a training accuracy of 77.52% and a validation accuracy of 83.33%. These compelling results highlight the potential of quantum circuits to serve as effective convolutional layers for feature extraction in image classification, especially with small datasets. Full article

(This article belongs to the Special Issue The Future of Quantum Machine Learning and Quantum AI)

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11 pages, 276 KiB

Open AccessArticle

Status of Electromagnetically Accelerating Universe

by Paul H. Frampton

Entropy 2024, 26(8), 629; https://doi.org/10.3390/e26080629 - 26 Jul 2024

Abstract

To describe the dark side of the universe, we adopt a novel approach where dark energy is explained as an electrically charged majority of dark matter. Dark energy, as such, does not exist. The Friedmann equation at the present time coincides with that [...] Read more.

To describe the dark side of the universe, we adopt a novel approach where dark energy is explained as an electrically charged majority of dark matter. Dark energy, as such, does not exist. The Friedmann equation at the present time coincides with that in a conventional approach, although the cosmological “constant” in the Electromagnetic Accelerating Universe (EAU) Model shares a time dependence with the matter component. Its equation of state is ω ≡ P/ρ ≡ −1 within observational accuracy. Full article

(This article belongs to the Special Issue Particle Theory and Theoretical Cosmology—Dedicated to Professor Paul Howard Frampton on the Occasion of His 80th Birthday)

29 pages, 2335 KiB

Open AccessArticle

Robust Support Vector Data Description with Truncated Loss Function for Outliers Depression

by Huakun Chen, Yongxi Lyu, Jingping Shi and Weiguo Zhang

Entropy 2024, 26(8), 628; https://doi.org/10.3390/e26080628 - 25 Jul 2024

Abstract

Support vector data description (SVDD) is widely regarded as an effective technique for addressing anomaly detection problems. However, its performance can significantly deteriorate when the training data are affected by outliers or mislabeled observations. This study introduces a universal truncated loss function framework [...] Read more.

Support vector data description (SVDD) is widely regarded as an effective technique for addressing anomaly detection problems. However, its performance can significantly deteriorate when the training data are affected by outliers or mislabeled observations. This study introduces a universal truncated loss function framework into the SVDD model to enhance its robustness and employs the fast alternating direction method of multipliers (ADMM) algorithm to solve various truncated loss functions. Moreover, the convergence of the fast ADMM algorithm is analyzed theoretically. Within this framework, we developed the truncated generalized ramp, truncated binary cross entropy, and truncated linear exponential loss functions for SVDD. We conducted extensive experiments on synthetic and real-world datasets to validate the effectiveness of these three SVDD models in handling data with different noise levels, demonstrating their superior robustness and generalization capabilities compared to other SVDD models. Full article

(This article belongs to the Special Issue Applications of Information Theory to Machine Learning)

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15 pages, 5652 KiB

Open AccessArticle

Flare Removal Model Based on Sparse-UFormer Networks

by Siqi Wu, Fei Liu, Yu Bai, Houzeng Han, Jian Wang and Ning Zhang

Entropy 2024, 26(8), 627; https://doi.org/10.3390/e26080627 - 25 Jul 2024

Abstract

When a camera lens is directly faced with a strong light source, image flare commonly occurs, significantly reducing the clarity and texture of the photo and interfering with image processing tasks that rely on visual sensors, such as image segmentation and feature extraction. [...] Read more.

When a camera lens is directly faced with a strong light source, image flare commonly occurs, significantly reducing the clarity and texture of the photo and interfering with image processing tasks that rely on visual sensors, such as image segmentation and feature extraction. A novel flare removal network, the Sparse-UFormer neural network, has been developed. The network integrates two core components onto the UFormer architecture: the mixed-scale feed-forward network (MSFN) and top-k sparse attention (TKSA), creating the sparse-transformer module. The MSFN module captures rich multi-scale information, enabling the more effective addressing of flare interference in images. The TKSA module, designed with a sparsity strategy, focuses on key features within the image, thereby significantly enhancing the precision and efficiency of flare removal. Furthermore, in the design of the loss function, besides the conventional flare, background, and reconstruction losses, a structural similarity index loss has been incorporated to ensure the preservation of image details and structure while removing the flare. Ensuring the minimal loss of image information is a fundamental premise for effective image restoration. The proposed method has been demonstrated to achieve state-of-the-art performance on the Flare7K++ test dataset and in challenging real-world scenarios, proving its effectiveness in removing flare artefacts from images. Full article

(This article belongs to the Section Complexity)

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23 pages, 3462 KiB

Open AccessArticle

Machine Learning Techniques for Blind Beam Alignment in mmWave Massive MIMO

by Aymen Ktari, Hadi Ghauch and Ghaya Rekaya-Ben Othman

Entropy 2024, 26(8), 626; https://doi.org/10.3390/e26080626 - 25 Jul 2024

Abstract

This paper proposes methods for Machine Learning (ML)-based Beam Alignment (BA), using low-complexity ML models, and achieves a small pilot overhead. We assume a single-user massive mmWave MIMO, Uplink, using a fully analog architecture. Assuming large-dimension codebooks of possible beam patterns at [...] Read more.

This paper proposes methods for Machine Learning (ML)-based Beam Alignment (BA), using low-complexity ML models, and achieves a small pilot overhead. We assume a single-user massive mmWave MIMO, Uplink, using a fully analog architecture. Assuming large-dimension codebooks of possible beam patterns at

U E

and

B S

, this data-driven and model-based approach aims to partially and blindly sound a small subset of beams from these codebooks. The proposed BA is blind (no CSI), based on Received Signal Energies (RSEs), and circumvents the need for exhaustively sounding all possible beams. A sub-sampled subset of beams is then used to train several ML models such as low-rank Matrix Factorization (MF), non-negative MF (NMF), and shallow Multi-Layer Perceptron (MLP). We provide an extensive mathematical description of these models and the algorithms for each of them. Our extensive numerical results show that, by sounding only

10 %

of the beams from the

U E

and

B S

codebooks, the proposed ML tools are able to accurately predict the non-sounded beams through multiple transmitted power regimes. This observation holds as the codebook sizes at

U E

and

B S

vary from

128 \times 128

to

1024 \times 1024

. Full article

(This article belongs to the Topic AI and Computational Methods for Modelling, Simulations and Optimizing of Advanced Systems: Innovations in Complexity)

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12 pages, 415 KiB

Open AccessArticle

Machine Learning-Based Risk Prediction of Discharge Status for Sepsis

by Kaida Cai, Yuqing Lou, Zhengyan Wang, Xiaofang Yang and Xin Zhao

Entropy 2024, 26(8), 625; https://doi.org/10.3390/e26080625 - 25 Jul 2024

Abstract

As a severe inflammatory response syndrome, sepsis presents complex challenges in predicting patient outcomes due to its unclear pathogenesis and the unstable discharge status of affected individuals. In this study, we develop a machine learning-based method for predicting the discharge status of sepsis [...] Read more.

As a severe inflammatory response syndrome, sepsis presents complex challenges in predicting patient outcomes due to its unclear pathogenesis and the unstable discharge status of affected individuals. In this study, we develop a machine learning-based method for predicting the discharge status of sepsis patients, aiming to improve treatment decisions. To enhance the robustness of our analysis against outliers, we incorporate robust statistical methods, specifically the minimum covariance determinant technique. We utilize the random forest imputation method to effectively manage and impute missing data. For feature selection, we employ Lasso penalized logistic regression, which efficiently identifies significant predictors and reduces model complexity, setting the stage for the application of more complex predictive methods. Our predictive analysis incorporates multiple machine learning methods, including random forest, support vector machine, and XGBoost. We compare the prediction performance of these methods with Lasso penalized logistic regression to identify the most effective approach. Each method’s performance is rigorously evaluated through ten iterations of 10-fold cross-validation to ensure robust and reliable results. Our comparative analysis reveals that XGBoost surpasses the other models, demonstrating its exceptional capability to navigate the complexities of sepsis data effectively. Full article

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15 pages, 436 KiB

Open AccessArticle

An Attacker–Defender Game Model with Constrained Strategies

by Jiaqi Ren, Jin Liu, Yibo Dong, Zhe Li and Weili Li

Entropy 2024, 26(8), 624; https://doi.org/10.3390/e26080624 - 24 Jul 2024

Abstract

Recently, research interest in the field of infrastructure attack and defense scenarios has increased. Numerous methods have been proposed for studying strategy interactions that combine complex network theory and game theory. However, the unavoidable effect of constrained strategies in complex situations has not [...] Read more.

Recently, research interest in the field of infrastructure attack and defense scenarios has increased. Numerous methods have been proposed for studying strategy interactions that combine complex network theory and game theory. However, the unavoidable effect of constrained strategies in complex situations has not been considered in previous studies. This study introduces a novel approach to analyzing these interactions by including the effects of constrained strategies, a factor often neglected in traditional analyses. First, we introduce the rule of constraints on strategies, which depends on the average distance between selected nodes. As the average distance increases, the probability of choosing the corresponding strategy decreases. Second, we establish an attacker–defender game model with constrained strategies based on the above rule and using information theory to evaluate the uncertainty of these strategies. Finally, we present a method for solving this problem and conduct experiments based on a target network. The results highlight the unique characteristics of the Nash equilibrium when setting constraints, as these constraints influence decision makers’ Nash equilibria. When considering the constrained strategies, both the attacker and the defender tend to select strategies with lower average distances. The effect of the constraints on their strategies becomes less apparent as the number of attackable or defendable nodes increases. This research advances the field by introducing a novel framework for examining strategic interactions in infrastructure defense and attack scenarios. By incorporating strategy constraints, our work offers a new perspective on the critical area of infrastructure security. Full article

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

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11 pages, 5644 KiB

Open AccessArticle

Tsallis q-Statistics Fingerprints in Precipitation Data across Sicily

by Vera Pecorino, Alessandro Pluchino and Andrea Rapisarda

Entropy 2024, 26(8), 623; https://doi.org/10.3390/e26080623 - 24 Jul 2024

Abstract

Precipitation patterns are critical for understanding the hydrological and climatological dynamics of any region. Sicily, the largest island in the Mediterranean sea, with its diverse topography and climatic conditions, serves as an ideal case study for analyzing precipitation data, to gain insights into [...] Read more.

Precipitation patterns are critical for understanding the hydrological and climatological dynamics of any region. Sicily, the largest island in the Mediterranean sea, with its diverse topography and climatic conditions, serves as an ideal case study for analyzing precipitation data, to gain insights into regional water resources, agricultural productivity, and climate change impacts. This paper employs advanced statistical physics methods, particularly Tsallis q-statistics, to analyze sub-hourly precipitation data from 2002 to 2023, provided by the Sicilian Agrometeorological Informative System (SIAS). We investigate several critical variables related to rainfall events, including duration, depth, maximum record, and inter-event time. The study spans two decades (2002–2012 and 2013–2023), analyzing the distributions of relevant variables. Additionally, we examine the simple returns of these variables to identify significant temporal changes, fitting these returns with q-Gaussian distributions. Our findings reveal the scale-invariant nature of precipitation events, the presence of long-range interactions, and memory effects, characteristic of complex environmental processes. Full article

(This article belongs to the Special Issue Nonadditive Entropies and Nonextensive Statistical Mechanics—Dedicated to Professor Constantino Tsallis on the Occasion of His 80th Birthday)

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12 pages, 437 KiB

Open AccessArticle

Making the Thermodynamic Cost of Active Inference Explicit

by Chris Fields, Adam Goldstein and Lars Sandved-Smith

Entropy 2024, 26(8), 622; https://doi.org/10.3390/e26080622 - 24 Jul 2024

Abstract

When describing Active Inference Agents (AIAs), the term “energy” can have two distinct meanings. One is the energy that is utilized by the AIA (e.g., electrical energy or chemical energy). The second meaning is so-called Variational Free Energy (VFE), a statistical quantity which [...] Read more.

When describing Active Inference Agents (AIAs), the term “energy” can have two distinct meanings. One is the energy that is utilized by the AIA (e.g., electrical energy or chemical energy). The second meaning is so-called Variational Free Energy (VFE), a statistical quantity which provides an upper bound on surprisal. In this paper, we develop an account of the former quantity—the Thermodynamic Free Energy (TFE)—and its relationship with the latter. We highlight the necessary tradeoffs between these two in a generic, quantum information-theoretic formulation, and the macroscopic consequences of those tradeoffs for the ways that organisms approach their environments. By making this tradeoff explicit, we provide a theoretical basis for the different metabolic strategies that organisms from plants to predators use to survive. 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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24 pages, 316 KiB

Open AccessArticle

A Field-Theory Approach for Modeling Dissipative Relativistic Fluids

by Nils Andersson, Thomas Celora, Gregory Comer and Ian Hawke

Entropy 2024, 26(8), 621; https://doi.org/10.3390/e26080621 - 24 Jul 2024

Abstract

We develop an action principle for producing a single-fluid two-constituent system with dissipation in general relativity. The two constituents in the model are particles and entropy. The particle flux creation rate is taken to be zero, while the entropy creation rate is non-zero. [...] Read more.

We develop an action principle for producing a single-fluid two-constituent system with dissipation in general relativity. The two constituents in the model are particles and entropy. The particle flux creation rate is taken to be zero, while the entropy creation rate is non-zero. Building on previous work, it is demonstrated that a new term (the proper time derivative of the matter space “metric”) is required in the Lagrangian in order to produce terms typically associated with bulk and shear viscosity. Equations of motion, entropy creation rate, and energy–momentum–stress tensor are derived. Using an Onsager approach of identifying thermodynamic “forces” and “fluxes”, a model is produced which delivers the same entropy creation rate as the standard, relativistic Navier–Stokes equations. This result is then contrasted with a model generated in the spirit of the action principle, which takes as its starting point a specific Lagrangian and then produces the equations of motion, entropy creation rate, and energy–momentum–stress tensor. Unlike the equations derived from Onsager reasoning, where the analogs of the bulk and shear viscosity coefficients are prescribed “externally”, we find that the forms of the coefficients in the second example are a direct result of the specified Lagrangian. Furthermore, the coefficients are shown to satisfy evolution equations along the fluid worldline, also a product of the specific Lagrangian. Full article

(This article belongs to the Section Statistical Physics)

8 pages, 648 KiB

Open AccessArticle

Molecular-Scale Liquid Density Fluctuations and Cavity Thermodynamics

by Attila Tortorella and Giuseppe Graziano

Entropy 2024, 26(8), 620; https://doi.org/10.3390/e26080620 - 24 Jul 2024

Abstract

Equilibrium density fluctuations at the molecular level produce cavities in a liquid and can be analyzed to shed light on the statistics of the number of molecules occupying observation volumes of increasing radius. An information theory approach led to the conclusion that these [...] Read more.

Equilibrium density fluctuations at the molecular level produce cavities in a liquid and can be analyzed to shed light on the statistics of the number of molecules occupying observation volumes of increasing radius. An information theory approach led to the conclusion that these probabilities should follow a Gaussian distribution. Computer simulations confirmed this prediction across various liquid models if the size of the observation volume is not large. The reversible work required to create a cavity and the chance of finding no molecules in a fixed observation volume are directly correlated. The Gaussian formula for the latter probability is scrutinized to derive the changes in enthalpy and entropy, which arise from the cavity creation. The reversible work of cavity creation has a purely entropic origin as a consequence of the solvent-excluded volume effect produced by the inaccessibility of a region of the configurational space. The consequent structural reorganization leads to a perfect compensation of enthalpy and entropy changes. Such results are coherent with those obtained from Lee in his direct statistical mechanical study. Full article

(This article belongs to the Special Issue Thermodynamics and Anomalous Properties in Fluids)

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