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8 pages, 467 KB  
Article
The Arrow of Time in Quantum Theory
by Jean-Patrick Connerade
Atoms 2025, 13(11), 86; https://doi.org/10.3390/atoms13110086 - 26 Oct 2025
Viewed by 293
Abstract
In Classical Mechanics, time is reversible, i.e., it implies no particular choice: only the observer knows in which direction it flows. The present article re-examines whether this remains true in Quantum Mechanics. In the context of Atomic Physics, it is concluded that the [...] Read more.
In Classical Mechanics, time is reversible, i.e., it implies no particular choice: only the observer knows in which direction it flows. The present article re-examines whether this remains true in Quantum Mechanics. In the context of Atomic Physics, it is concluded that the existence of an arrow of time depends on the manner in which the radiation field is introduced, which must be non-perturbative. Full article
11 pages, 695 KB  
Article
Revisiting the Origin of the Universe and the Arrow of Time
by Takeshi Fukuyama
Symmetry 2025, 17(10), 1688; https://doi.org/10.3390/sym17101688 - 9 Oct 2025
Viewed by 469
Abstract
In this paper, we reconsider two long-standing yet unsolved problems: the origin of the universe and the arrow of time. We show that only a closed universe is free from singularities and that the arrow of time is symmetric with respect to the [...] Read more.
In this paper, we reconsider two long-standing yet unsolved problems: the origin of the universe and the arrow of time. We show that only a closed universe is free from singularities and that the arrow of time is symmetric with respect to the universe’s maximum scale. The Wheeler–DeWitt equation is explicitly solved to obtain local dynamical times. It is shown that the thermodynamic arrow of time coincides with both the dynamical time and the cosmological (expanding universe) time. This correspondence is explicitly demonstrated in two-dimensional spacetime. Full article
(This article belongs to the Section Physics)
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17 pages, 3560 KB  
Article
Virtual Reality Driving Simulator: Investigating the Effectiveness of Image–Arrow Aids in Improving the Performance of Trainees
by Numan Ali, Muhammad Alyan Ansari, Dawar Khan, Hameedur Rahman and Sehat Ullah
Future Transp. 2025, 5(4), 130; https://doi.org/10.3390/futuretransp5040130 - 1 Oct 2025
Viewed by 554
Abstract
Virtual reality driving simulators have been increasingly used for training purposes, but they are still lacking effective driver assistance features, and poor use of user interface (UI) and guidance systems leads to users’ performance being affected. In this paper, we investigate image–arrow aids [...] Read more.
Virtual reality driving simulators have been increasingly used for training purposes, but they are still lacking effective driver assistance features, and poor use of user interface (UI) and guidance systems leads to users’ performance being affected. In this paper, we investigate image–arrow aids in a virtual reality driving simulator (VRDS) that enables trainees (new drivers) to interpret instructions according to the correct course of action while performing their driving task. Image–arrow aids consist of arrows, texts, and images that are separately rendered during driving in the VRDS. A total of 45 participants were divided into three groups: G1 (image–arrow aids), G2 (audio and textual aids), and G3 (arrows and textual aids). The results showed that G1 (image–arrow guidance) achieved the best performance, with a mean error rate of 8.1 (SD = 1.23) and a mean completion time of 3.26 min (SD = 0.56). In comparison, G2 (audio and textual aids) had a mean error rate of 10.8 (SD = 1.31) and completion time of 4.49 min (SD = 0.67), while G3 (arrows and textual aids) had the highest error rate (18.4, SD = 1.43) and longest completion time (6.51 min, SD = 0.68). An evaluation revealed that the performance of G1 is significantly better than that of G2 and G3 in terms of performance measures (errors + time) and subjective analysis such as usability, easiness, understanding, and assistance. Full article
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16 pages, 250 KB  
Article
Emptiness Is to Womanism as Purple Is to Lavender: Buddhist Womanism Revisited in Alice Walker’s Taking the Arrow Out of the Heart
by Zhi Huang and Zier Zhuang
Religions 2025, 16(9), 1174; https://doi.org/10.3390/rel16091174 - 11 Sep 2025
Viewed by 442
Abstract
This paper argues that the philosophy of Buddhist emptiness not only finds expression in Alice Walker’s Taking the Arrow Out of the Heart with its two most salient manifestationsdependent origination and impermanence, but is applied to alleviate suffering in the poetry, and the [...] Read more.
This paper argues that the philosophy of Buddhist emptiness not only finds expression in Alice Walker’s Taking the Arrow Out of the Heart with its two most salient manifestationsdependent origination and impermanence, but is applied to alleviate suffering in the poetry, and the two approaches the poetry collection are (1) to recognize emptiness in times of crisis and (2) to cultivate bodhicitta through using emptiness to extend loving kindness to all beings. Furthermore, it is argued that emptiness enriches Buddhist womanism by strengthening its theoretical underpinnings, redirecting the focus from practice to cognitive transformation, and harmonizing the priorities of individual and communal wellbeing. Full article
(This article belongs to the Special Issue Religion, Gender and Social Development)
16 pages, 1196 KB  
Article
Rapid On-Field Monitoring for Odor-Active Homologous Aliphatic Aldehydes and Ketones from Hot-Mix Asphalt Emission via Dynamic-SPME Air Sampling with Online Gas Chromatographic Analysis
by Stefano Dugheri, Giovanni Cappelli, Ilaria Rapi, Riccardo Gori, Lorenzo Venturini, Niccolò Fanfani, Chiara Vita, Fabio Cioni, Ettore Guerriero, Domenico Cipriano, Gian Luca Bartolucci, Luca Di Giampaolo, Mieczyslaw Sajewicz, Veronica Traversini, Nicola Mucci and Antonio Baldassarre
Molecules 2025, 30(17), 3545; https://doi.org/10.3390/molecules30173545 - 29 Aug 2025
Viewed by 707
Abstract
Odorous emissions from hot-mix asphalt (HMA) plants are a growing environmental concern, particularly due to airborne aldehydes and ketones, which have low odor thresholds and a strong sensory impact. This study presents a field-ready analytical method for monitoring odor-active volatile compounds. The system [...] Read more.
Odorous emissions from hot-mix asphalt (HMA) plants are a growing environmental concern, particularly due to airborne aldehydes and ketones, which have low odor thresholds and a strong sensory impact. This study presents a field-ready analytical method for monitoring odor-active volatile compounds. The system uses dynamic solid-phase microextraction (SPME and SPME Arrow) with on-fiber derivatization via O-(2,3,4,5,6-pentafluorobenzyl)hydroxylamine (PFBHA) and is coupled to gas chromatography–mass spectrometry (GC–MS) for direct detection. A flow-cell sampling unit enables the real-time capture of aliphatic aldehydes and ketones under transient emission conditions. Calibration using permeation tubes demonstrated sensitivity (limits of detection (LODs) below 0.13 μg/m3), recovery above 85% and consistent reproducibility. Compound identity was confirmed using retention indices and fragmentation patterns. Uncertainty assessment followed ISO GUM (Guide to the Expression of Uncertainty in Measurement) standards, thereby validating the method’s environmental applicability. Field deployment 200 m from an HMA facility identified measurable concentrations that aligned with CALPUFF model predictions. The method’s dual-isomer resolution and 10 min runtime make it ideal for responding to time-sensitive odor complaints. Overall, this approach supports regulatory efforts by enabling high-throughput on-site chemical monitoring and improving source attribution in cases of odor nuisance. Full article
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20 pages, 335 KB  
Article
Arrow of Time in Quantum Mechanics and Set Theory
by Jerzy Król
Entropy 2025, 27(9), 904; https://doi.org/10.3390/e27090904 - 26 Aug 2025
Viewed by 840
Abstract
The set-theory twist of quantum mechanics uncovers forcing in axiomatic Zermelo–Fraenkel set theory as a viable tool to understand the singularities in a physical spacetime and serves as a link between the quantum and classical worlds. The random forcing explains the emergence of [...] Read more.
The set-theory twist of quantum mechanics uncovers forcing in axiomatic Zermelo–Fraenkel set theory as a viable tool to understand the singularities in a physical spacetime and serves as a link between the quantum and classical worlds. The random forcing explains the emergence of time in quantum mechanics on infinite-dimensional Hilbert spaces. A natural flow of randomness from fully random to deterministic and classical, as in the measurement procedure and the decoherence process, becomes responsible for the cosmological arrow of time and also for the local-coordinate time in spacetime. Full article
(This article belongs to the Special Issue Quantum Mechanics and the Challenge of Time)
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14 pages, 7028 KB  
Article
Flavor Profile of Tomatoes Across Different Cultivation Times Based on GC × GC-Q/TOFMS
by Yuan Gao, Nan Jiang, Jing Liu, Guanglu Cui, Meng Zhao, Yuanfang Du, Hua Ping and Cheng Li
Foods 2025, 14(17), 2975; https://doi.org/10.3390/foods14172975 - 26 Aug 2025
Viewed by 798
Abstract
Volatile compounds greatly affect tomato aroma, but systematic analysis of volatiles in tomatoes is limited by detection techniques. Here, HS-SPME Arrow-GC × GC-Q/TOFMS was employed to analyze tomato flavor profiles across different cultivation times. To investigate the effects of light and temperature on [...] Read more.
Volatile compounds greatly affect tomato aroma, but systematic analysis of volatiles in tomatoes is limited by detection techniques. Here, HS-SPME Arrow-GC × GC-Q/TOFMS was employed to analyze tomato flavor profiles across different cultivation times. To investigate the effects of light and temperature on aroma profiles, three tomato samples across different cultivation periods, including S1 (harvested on May 30th, with lowest temperature and light conditions), S2 (harvested on August 10th, with the highest temperature and light), and S3 (harvested on June 27th, with moderate temperature and light), were analyzed. Overall, 227 volatiles were identified, belonging to 9 aroma categories. Hexanal, (E)-2-hexenal, nonanal, (E)-2-Octenal, trans-geranylacetone, 6-methyl-5-hepten-2-one, 3,4-Octadiene, 7-methyl-, and citral were found to be the key volatiles contributing most significantly to differentiating the samples across cultivation periods, imparting grassy and floral–fruity notes, respectively. The S1 tomatoes had a distinct grassy aroma, whereas the S3 tomatoes had a floral/fruity fragrance. Most differential metabolites were correlated with fatty acid, amino acid, and isoprenoid pathways. S1 tomatoes were characterized by fatty aldehydes (mainly C6/C9), and S2 tomatoes contained high concentrations of fatty alcohols. S3 tomatoes were positively correlated with isoprenoid-derived volatiles. These variations might be caused by the fluctuations in daily temperature and light intensity. This work establishes a foundational reference for assessing environmental effects on tomato flavor profiles. Full article
(This article belongs to the Section Food Analytical Methods)
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23 pages, 8223 KB  
Article
Evaluating Visual eHMI Formats for Pedestrian Crossing Confirmation in Electric Autonomous Vehicles: A Comprehension-Time Study with Simulation and Preliminary Field Validation
by Nuksit Noomwongs, Natchanon Kitpramongsri, Sunhapos Chantranuwathana and Gridsada Phanomchoeng
World Electr. Veh. J. 2025, 16(9), 485; https://doi.org/10.3390/wevj16090485 - 25 Aug 2025
Viewed by 921
Abstract
Effective communication between electric autonomous vehicles (EAVs) and pedestrians is critical for safety, yet the absence of a driver removes traditional cues such as eye contact or gestures. While external human–machine interfaces (eHMIs) have been proposed, few studies have systematically compared visual formats [...] Read more.
Effective communication between electric autonomous vehicles (EAVs) and pedestrians is critical for safety, yet the absence of a driver removes traditional cues such as eye contact or gestures. While external human–machine interfaces (eHMIs) have been proposed, few studies have systematically compared visual formats across demographic groups and validated findings in both simulation and real-world settings. This study addresses this gap by evaluating various eHMI designs using combinations of textual cues (“WALK” and “CROSS”), symbolic indicators (pedestrian and arrow icons), and display colors (white and green). Twenty simulated scenarios were developed in the CARLA simulator, where 100 participants observed an EAV equipped with eHMIs and responded by pressing a button upon understanding the vehicle’s intention. The results showed that green displays facilitated faster comprehension than white, “WALK” was understood more quickly than “CROSS,” and pedestrian symbols outperformed arrows in clarity. The fastest overall comprehension occurred with the green pedestrian symbol paired with the word “WALK.” A subsequent field experiment using a Level 3 autonomous vehicle with a smaller participant group and differing speed/distance conditions provided preliminary support for the consistency of these observed trends. The novelty of this work lies in combining simulation with preliminary field validation, using comprehension time as the primary metric, and comparing results across four age groups to derive evidence-based eHMI design recommendations. These findings offer practical guidance for enhancing pedestrian safety, comprehension, and trust in EAV–pedestrian interactions. Full article
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11 pages, 714 KB  
Article
Active Microbiological Surveillance for Contrasting Multi-Drug-Resistant Pathogens: Comparison Between a Multiplex Real-Time PCR Method and Culture
by Gaetano Maugeri, Maddalena Calvo, Guido Scalia and Stefania Stefani
Diagnostics 2025, 15(17), 2128; https://doi.org/10.3390/diagnostics15172128 - 22 Aug 2025
Viewed by 662
Abstract
Background/Objectives. Multi-drug-resistant (MDR) microorganisms pose a significant challenge in healthcare settings, particularly with beta-lactam-resistant Gram-negative bacteria and glycopeptide-resistant enterococci. Culture represents the most reliable technique in determining their presence within surveillance swabs. However, it requires a long time-to-result (TTR) and shows low [...] Read more.
Background/Objectives. Multi-drug-resistant (MDR) microorganisms pose a significant challenge in healthcare settings, particularly with beta-lactam-resistant Gram-negative bacteria and glycopeptide-resistant enterococci. Culture represents the most reliable technique in determining their presence within surveillance swabs. However, it requires a long time-to-result (TTR) and shows low sensitivity. Molecular techniques integrate diagnostic procedures, allowing TTR reduction and precise identification of genes. Methods. During our usual surveillance campaign, we had the opportunity to evaluate the Allplex Entero-DR assay (Seegene Inc., Seoul, Republic of Korea) and the Entero-DR Plus assay (Arrow Diagnostics srl, Genova, Italy) molecular kits for the detection of extended-β-lactamases (ESBL), carbapenem- and vancomycin-resistant genes, as well as Acinetobacter spp. and Pseudomonas aeruginosa spp. identification directly from rectal swabs. A comparison between these tests and the culture-based routine completed the study. Results. The analysis included 300 rectal swabs from the University Hospital Policlinico (Catania, Italy). One hundred and eighty-eight samples (62.6%) resulted as positive for at least one Allplex™ target, reaching optimal sensitivity and negative predictive value (100%). Our results underlined the ubiquitous blaCTX-M and van genes presence and demonstrated the diffusion of double-carbapenemases genes and metallo-β-lactamases-producing strains. In our epidemiological setting, few data were collected about carbapenem-resistant P. aeruginosa and Acinetobacter spp., which require further evaluations on simultaneous respiratory colonization and higher sample numbers. Conclusions. Our analysis highlighted the importance of combining conventional and advanced diagnostic methods in investigating MDR pathogens. The right approach should be based on the prevalence and variability of resistance mechanisms within a specific epidemiological area. Remarkably, molecular screenings may exclude negative samples within high-risk areas due to a significant negative predictive value. Full article
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24 pages, 756 KB  
Article
Complex Time Approach to the Hamiltonian and the Entropy Production of the Damped Harmonic Oscillator
by Kyriaki-Evangelia Aslani
Entropy 2025, 27(8), 883; https://doi.org/10.3390/e27080883 - 21 Aug 2025
Viewed by 1109
Abstract
The present work applies and extends the previously developed Quantitative Geometrical Thermodynamics (QGT) formalism to the derivation of a Hamiltonian for the damped harmonic oscillator (DHO) across all damping regimes. By introducing complex time, with the real part encoding entropy production and the [...] Read more.
The present work applies and extends the previously developed Quantitative Geometrical Thermodynamics (QGT) formalism to the derivation of a Hamiltonian for the damped harmonic oscillator (DHO) across all damping regimes. By introducing complex time, with the real part encoding entropy production and the imaginary part governing reversible dynamics, QGT provides a unified geometric framework for irreversible thermodynamics, showing that the DHO Hamiltonian can be obtained directly from the (complex) entropy production in a simple exponential form that is generalized across all damping regimes. The derived Hamiltonian preserves a modified Poisson bracket structure and embeds thermodynamic irreversibility into the system’s evolution. Moreover, the resulting expression coincides in form with the well-known Caldirola–Kanai Hamiltonian, despite arising from fundamentally different principles, reinforcing the validity of the QGT approach. The results are also compared with the GENERIC framework, showing that QGT offers an elegant alternative to existing approaches that maintains consistency with symplectic geometry. Furthermore, the imaginary time component is interpreted as isomorphic to the antisymmetric Poisson matrix through the lens of geometric algebra. The formalism opens promising avenues for extending Hamiltonian mechanics to dissipative systems, with potential applications in nonlinear dynamics, quantum thermodynamics, and spacetime algebra. Full article
(This article belongs to the Special Issue Geometry in Thermodynamics, 4th Edition)
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23 pages, 1890 KB  
Article
Executive Function and Transfer Effect Training in Children: A Behavioral and Event-Related Potential Pilot Study
by Chen Cheng and Baoxi Wang
Behav. Sci. 2025, 15(7), 956; https://doi.org/10.3390/bs15070956 - 15 Jul 2025
Viewed by 2295
Abstract
This study examined the effect of executive function training targeting both updating and inhibition in children. The training included both single training (i.e., number 2-back training) and combined training (i.e., number 2-back and fish flanker training). Event-related potentials were also recorded. In Experiment [...] Read more.
This study examined the effect of executive function training targeting both updating and inhibition in children. The training included both single training (i.e., number 2-back training) and combined training (i.e., number 2-back and fish flanker training). Event-related potentials were also recorded. In Experiment 1, we employed both single-training and combined-training groups, which were contrasted with each other and with an active control group. In Experiment 2, the control group and the combined-training group were recruited to perform training tasks identical to those used in Experiment 1, and their EEG data were collected during the pretest and posttest stage. Experiment 1 found that the single group showed clear evidence for transfer to letter 2-back task compared with the active control group. The combined group showed significant transfer to the letter 2-back and arrow flanker task. Both groups found no transfer to fluid intelligence or shifting. Experiment 2 revealed that the participants who received updating and inhibition training showed a significant reduction in N2 amplitude and a significant increase in P300 amplitude after training in comparison to the active control group. Importantly, there was a significant positive correlation between reduced N2 amplitude and decreased response time in conflict effects. Additionally, there was a strong positive trend toward a relationship between behavioral performance improvement and an increase in P300 amplitude. From the perspective of the near-transfer effect, combined training is more effective than single training. Our results showed that the extent of transfer depends on the cognitive component overlap between the training and transfer tasks. Full article
(This article belongs to the Section Experimental and Clinical Neurosciences)
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19 pages, 1419 KB  
Article
Revisiting the Relationship Between the Scale Factor (a(t)) and Cosmic Time (t) Using Numerical Analysis
by Artur Chudzik
Mathematics 2025, 13(14), 2233; https://doi.org/10.3390/math13142233 - 9 Jul 2025
Viewed by 1226
Abstract
Background: Current cosmological fits typically assume a direct relation between cosmic time (t) and the scale factor (a(t)), yet this ansatz remains largely untested across diverse observations. Objectives: We (i) test whether a single power-law scaling [...] Read more.
Background: Current cosmological fits typically assume a direct relation between cosmic time (t) and the scale factor (a(t)), yet this ansatz remains largely untested across diverse observations. Objectives: We (i) test whether a single power-law scaling (a(t)tα) can reproduce late- and early-time cosmological data and (ii) explore whether a dynamically evolving (α(t)), modeled as a scalar–tensor field, naturally induces directional asymmetry in cosmic evolution. Methods: We fit a constant-α model to four independent datasets: 1701 Pantheon+SH0ES supernovae, 162 gamma-ray bursts, 32 cosmic chronometers, and the Planck 2018 TT spectrum (2507 points). The CMB angular spectrum is mapped onto a logarithmic distance-like scale (μ=log10D), allowing for unified likelihood analysis. Each dataset yields slightly different preferred values for H0 and α; therefore, we also perform a global combined fit. For scalar–tensor dynamics, we integrate α(t) under three potentials—quadratic, cosine, and parity breaking (α3sinα)—and quantify directionality via forward/backward evolution and Lyapunov exponents. Results: (1) The constant-α model achieves good fits across all datasets. In combined analysis, it yields H070kms1Mpc1 and α1.06, outperforming ΛCDM globally (ΔAIC401254), though ΛCDM remains favored for some low-redshift chronometer data. High-redshift GRB and CMB data drive the improved fit. Numerical likelihood evaluations are approximately three times faster than for ΛCDM. (2) Dynamical α(t) models exhibit time-directional behavior: under asymmetric potentials, forward evolution displays finite Lyapunov exponents (λL103), while backward trajectories remain confined (λL<0), realizing classical arrow-of-time emergence without entropy or quantum input. Limitations: This study addresses only homogeneous background evolution; perturbations and physical derivations of potentials remain open questions. Conclusions: The time-scaling approach offers a computationally efficient control scenario in cosmological model testing. Scalar–tensor extensions naturally introduce classical time asymmetry that is numerically accessible and observationally testable within current datasets. Code and full data are available. Full article
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22 pages, 1208 KB  
Article
Weak Sustainability at Regional Scale
by Alan Randall, Mackenzie Jones and Elena G. Irwin
Sustainability 2025, 17(12), 5403; https://doi.org/10.3390/su17125403 - 11 Jun 2025
Viewed by 696
Abstract
Weak sustainability (WS) requires that the inclusive wealth (IW) of a place (e.g., the world, a nation, or a sub-national region) be non-decreasing over a long time. The WS framework provides a more complete account of the sustainability of a place than do [...] Read more.
Weak sustainability (WS) requires that the inclusive wealth (IW) of a place (e.g., the world, a nation, or a sub-national region) be non-decreasing over a long time. The WS framework provides a more complete account of the sustainability of a place than do sustainability indicators or conventional economic measures, such as gross domestic product. However, while many decisions that affect sustainability are made at regional and local levels, the abstract theory of WS was developed without explicit recognition of the porosity of geographic boundaries and the interdependencies of regions. In this paper, we make three contributions: a carefully reasoned defense of IW per capita as the WS criterion, an improved understanding of the relationship between mobility, labor productivity, and regional economic growth, and an empirical application to US counties that demonstrates the feasibility of empirical regional WS assessment by summarizing Jones’ research. This analysis, extending the framework developed by Arrow and co-authors, accounts for more region-specific factors related to population, most notably the labor productivity component of health capital, and assesses IW per capita for all 50 states and 3108 counties in the US from 2010 to 2017. These improved methods revealed substantially more states and counties that were not WS relative to results using the Arrow et al. framework. The not-WS counties exhibited a distinct rural bias, as regional scientists have suspected but, nevertheless, the majority of rural counties were WS. Our work demonstrated that regional WS assessment is feasible, produces results that are consistent with prior expectations based on reasoning and empirical research, and has the potential to provide fresh insights into longstanding questions of regional development. Full article
(This article belongs to the Section Sustainable Products and Services)
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30 pages, 5512 KB  
Article
Making Autonomous Taxis Understandable: A Comparative Study of eHMI Feedback Modes and Display Positions for Pickup Guidance
by Gang Ren, Zhihuang Huang, Yaning Zhu, Wenshuo Lin, Tianyang Huang, Gang Wang and Jeehang Lee
Electronics 2025, 14(12), 2387; https://doi.org/10.3390/electronics14122387 - 11 Jun 2025
Viewed by 801
Abstract
Passengers often struggle to identify intended pickup locations when autonomous taxis (ATs) arrive, leading to confusion and delays. While prior external human–machine interface (eHMI) studies have focused on pedestrian crossings, few have systematically compared feedback modes and display positions for AT pickup guidance [...] Read more.
Passengers often struggle to identify intended pickup locations when autonomous taxis (ATs) arrive, leading to confusion and delays. While prior external human–machine interface (eHMI) studies have focused on pedestrian crossings, few have systematically compared feedback modes and display positions for AT pickup guidance at varying distances. This study investigates the effectiveness of three eHMI feedback modes (Eye, Arrow, and Number) displayed at two positions (Body and Top) for communicating AT pickup locations. Through a controlled virtual reality experiment, we examined how these design variations impact user performance across key metrics including selection time, error rates, and decision confidence across varied parking distances. The results revealed distinct advantages for each feedback mode: Number feedback provided the fastest response times, particularly when displayed at the top position; Arrow feedback facilitated more confident decisions with lower error rates in close-range scenarios; and Eye feedback demonstrated superior performance in distant conditions by preventing severe identification errors. Body position displays consistently outperformed top-mounted ones, improving users’ understanding of the vehicle’s intended actions. These findings highlight the importance of context-aware eHMI systems that dynamically adapt to interaction distances and operational requirements. Based on our evidence, we propose practical design strategies for implementing these feedback modes in real-world AT services to optimize both system efficiency and user experience in urban mobility environments. Future work should address user learning challenges and validate these findings across diverse environmental conditions and implementation frameworks. Full article
(This article belongs to the Section Computer Science & Engineering)
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16 pages, 357 KB  
Article
Entropy Maximization, Time Emergence, and Phase Transition
by Jonathan Smith
Entropy 2025, 27(6), 586; https://doi.org/10.3390/e27060586 - 30 May 2025
Viewed by 692
Abstract
We survey developments in the use of entropy maximization for applying the Gibbs Canonical Ensemble to finite situations. Biological insights are invoked along with physical considerations. In the game-theoretic approach to entropy maximization, the interpretation of the two player roles as predator and [...] Read more.
We survey developments in the use of entropy maximization for applying the Gibbs Canonical Ensemble to finite situations. Biological insights are invoked along with physical considerations. In the game-theoretic approach to entropy maximization, the interpretation of the two player roles as predator and prey provides a well-justified and symmetric analysis. The main focus is placed on the Lagrange multiplier approach. Using natural physical units with Planck’s constant set to unity, it is recognized that energy has the dimensions of inverse time. Thus, the conjugate Lagrange multiplier, traditionally related to absolute temperature, is now taken with time units and oriented to follow the Arrow of Time. In quantum optics, where energy levels are bounded above and below, artificial singularities involving negative temperatures are eliminated. In a biological model where species compete in an environment with a fixed carrying capacity, use of the Canonical Ensemble solves an instance of Eigen’s phenomenological rate equations. The Lagrange multiplier emerges as a statistical measure of the ecological age. Adding a weak inequality on an order parameter for the entropy maximization, the phase transition from initial unconstrained growth to constrained growth at the carrying capacity is described, without recourse to a thermodynamic limit for the finite system. Full article
(This article belongs to the Section Thermodynamics)
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