Search Results (169)

The general framework of Entropic Dynamics (ED) is used to construct non-relativistic models of relational Quantum Mechanics from well-known inference principles—probability, entropy and information geometry. Although only partially relational—the absolute structures of simultaneity and Euclidean geometry are still retained—these models provide a useful testing ground for ideas that will prove useful in the context of more realistic relativistic theories. The fact that in ED the positions of particles have definite values, just as in classical mechanics, has allowed us to adapt to the quantum case some intuitions from Barbour and Bertotti’s classical framework. Here, however, we propose a new measure of the mismatch between successive states that is adapted to the information metric and the symplectic structures of the quantum phase space. We make explicit that ED is temporally relational and we construct non-relativistic quantum models that are spatially relational with respect to rigid translations and rotations. The ED approach settles the longstanding question of what form the constraints of a classical theory should take after quantization: the quantum constraints that express relationality are to be imposed on expectation values. To highlight the potential impact of these developments, the non-relativistic quantum model is parametrized into a generally covariant form and we show that the ED approach evades the analogue of what in quantum gravity has been called the problem of time. Full article

This longitudinal study applies decade-spanning socioeconomic indicators (2013–2022) from the Beijing–Tianjin–Hebei urban agglomeration. An integrated analytical framework was developed, merging the super-efficiency slack-based measurement (SBM) methodology with entropic weighting techniques to quantify tourism efficiency and economic development. Subsequent phases employed a multi-method analytical cascade: coupling coordination assessment modeling for system interaction analysis, standard deviation ellipses for spatial dispersion characterization, and Markovian transition matrices for temporal pattern identification. The investigation concludes with evolutionary trajectory projections using gray system forecasting GM(1,1) modeling. The analytical findings reveal the following patterns: (1) Within the Beijing–Tianjin–Hebei metropolitan cluster, tourism efficiency demonstrates a consistent upward trajectory, manifesting spatial differentiation characteristics characterized by a dual-core structure centered on Tianjin and Baoding, with higher values observed in northwestern areas compared to southeastern regions. Concurrently, regional disparities exhibit progressive convergence over temporal progression. (2) The level of economic development in the Beijing–Tianjin–Hebei city cluster has been rising steadily, demonstrating a geospatial distribution of ‘central concentration with peripheral attenuation, with the north-east being better than the southwest’, and the gap between the regional differences has become broader over time. (3) The coupling between tourism efficiency and the level of economic development in the Beijing–Tianjin–Hebei city cluster has generally improved, with Beijing and Tianjin predominantly in a coordinated regime, and some cities in Hebei Province about to shift from dysfunctional to coordinated, and, spatially, the coupling and coordination in northern sectors demonstrate superior performance compared to southern counterparts nationally. (4) The coupling coordination degree of the Beijing–Tianjin–Hebei city cluster in the next eight years is predicted by the gray GM(1,1) prediction model and the overall continuation of the growth trend of the Beijing–Tianjin–Hebei city cluster over the past ten years, thus verifying the importance of the regional integrated policy frameworks in the system integration of the Beijing–Tianjin–Hebei metropolitan system. Full article

Hybrid quantum–classical systems are emerging as key platforms in quantum computing, sensing, and communication technologies, but the quantum–classical interface (QCI)—the boundary enabling these systems—introduces unique and largely unexplored security vulnerabilities. This position paper proposes using entropy-based metrics to monitor and enhance security, specifically at the QCI. We present a theoretical security outline that leverages well-established information-theoretic entropy measures, such as Shannon entropy, von Neumann entropy, and quantum relative entropy, to detect anomalous behaviors and potential breaches at the QCI. By linking entropy fluctuations to scenarios of practical relevance—including quantum key distribution, quantum sensing, and hybrid control systems—we promote the potential value and applicability of entropy-based security monitoring. While explicitly acknowledging practical limitations and theoretical assumptions, we argue that entropy-based metrics provide a complementary approach to existing security methods, inviting further empirical studies and theoretical refinements that can strengthen future quantum technologies. Full article

A total of 108 maximum Kolmogorov entropy (S_K) values, calculated by means of chaos theory, are obtained from 108 time series (TSs) (each consisting of 28,463 hourly data points). The total TSs are divided into 54 urban meteorological (temperature (T), relative humidity (RH) and wind speed magnitude (WS)) and 54 pollutants (PM₁₀, PM_2.5 and CO). The measurement locations (6) are located at different heights and the data recording was carried out in three periods, 2010–2013, 2017–2020 and 2019–2022, which determines a total of 3,074,004 data points. For each location, the sum of the maximum entropies of urban meteorology and the sum of maximum entropies of pollutants, S_{K, MV} and S_{K, P}, are calculated and plotted against h, generating six different curves for each of the three data-recording periods. The tangent of each figure is determined and multiplied by the average temperature value of each location according to the period, obtaining, in a first approximation, the magnitude of the entropic forces associated with urban meteorology (F_{K, MV}) and pollutants (F_{K, P}), respectively. It is verified that all the time series have a fractal dimension, and that the fractal dimension of the pollutants shows growth towards the most recent period. The entropic dynamics of pollutants is more dominant with respect to the dynamics of urban meteorology. It is found that this greater influence favors subdiffusion processes (α < 1), which is consistent with a geographic basin with lower atmospheric resilience. By applying a heavy-tailed probability density analysis, it is shown that atmospheric pollution states are more likely, generating an extreme environment that favors the growth of respiratory diseases and low relative humidity, makes heat islands more stable over time, and strengthens heat waves. Full article

The review presents arguments emphasizing the importance of using the entropic measure of time (EMT) in the study of irreversible evolving systems. The possibilities of this measure for obtaining the laws of system evolution are shown. It is demonstrated that EMT provides a novel and unified perspective on the principle of maximum entropy production (MEPP), which is established in the physics of irreversible processes, as well as on the laws of growth and evolution proposed in biology. Essentially, for irreversible processes, the proposed approach allows, in a certain sense, to identify concepts such as the duration of existence, MEPP, and natural selection. EMT has been used to generalize prior results, indicating that the intrinsic time of a system is logarithmically dependent on extrinsic (Newtonian) time. Full article

In the past, measures of the “Earth-likeness” of exoplanets have been qualitative, considering an abiotic Earth, or requiring discretionary choices of what parameters make a planet Earth-like. With the advent of high-resolution exoplanet spectroscopy, there is a growing need for a method of quantifying the Earth-likeness of a planet that addresses these issues while making use of the data available from modern telescope missions. In this work, we introduce an informational–entropic metric that makes use of the spectrum of an exoplanet to directly quantify how Earth-like the planet is. To illustrate our method, we generate simulated transmission spectra of a series of Earth-like and super-Earth exoplanets, as well as an exoJupiter and several gas giant exoplanets. As a proof of concept, we demonstrate the ability of the information metric to evaluate how similar a planet is to Earth, making it a powerful tool in the search for a candidate Earth 2.0. Full article

We introduce a new coherent risk measure, the minimal-entropy risk measure, which is built on the minimal-entropy $\sigma$-martingale measure—a concept inspired by the well-known minimal-entropy martingale measure used in option pricing. While the minimal-entropy martingale measure is commonly used for pricing and hedging, the minimal-entropy $\sigma$-martingale measure has not previously been studied, nor has it been analyzed as a traditional risk measure. We address this gap by clearly defining this new risk measure and examining its fundamental properties. In addition, we revisit the entropic risk measure, typically expressed through an exponential formula. We provide an alternative definition using a supremum over Kullback–Leibler divergences, making its connection to entropy clearer. We verify important properties of both risk measures, such as convexity and coherence, and extend these concepts to dynamic situations. We also illustrate their behavior in scenarios involving optimal risk transfer. Our results link entropic concepts with incomplete-market pricing and demonstrate how both risk measures share a unified entropy-based foundation. Full article

This study presents a detailed thermodynamic investigation on the protonation behavior of tartronic acid in aqueous solutions of various ionic media, including sodium chloride, potassium chloride, tetramethylammonium chloride, and tetraethylammonium iodide. Specifically, potentiometric measurements were performed at temperatures ranging from 288.15 to 310.15 K and ionic strengths between 0.1 and 1.0 mol dm⁻³ to determine stoichiometric protonation constants in different ionic media. The formation of weak complexes between tartronate and alkaline metal cations was obtained by means of the ΔpK method. Moreover, data were modeled using the Debye–Hückel equation and Specific Ion Interaction Theory (SIT), allowing for the calculation of standard thermodynamic parameters and the assessment of the dependence of protonation constants on ionic strength. Additionally, the protonation behavior of tartronic acid was compared with that of structurally related acids, such as malonic and mesoxalic acids, providing insights into the role of molecular structure in acid dissociation. The results emphasize the significant role of entropic contributions in the protonation process and provide a comprehensive model for the thermodynamic properties of tartronic acid across a wide range of experimental conditions. Full article

In three periods of 3.25 years each, and at the same six different heights of a basin geomorphology, measurements were made, in the form of a time series, of urban meteorological variables (MV) (temperature, relative humidity, wind speed magnitude) and pollutants (P) (PM₁₀, PM_2.5, and CO). It is verified that each time series has a fractal dimension, and the value of its maximum Kolmogorov entropy is determined. These values generate two entropic surfaces according to measurement periods: one for urban meteorology and another for pollutants. The calculation of the gradient to each entropic surface multiplied by the average temperature of the period according to the measurement location gives, approximately, the average entropic force for each location. Combining these results with an analysis of the ratio between urban meteorological entropies and pollutant entropies, it is shown that in a basin morphology the entropic forces associated with pollutants are dominant, a source of heat, and there is a high probability that they produce extreme events. This condition also favors anomalous subdiffusion. Full article

When examined at the nanometer length scale, metallic liquids exhibit extensive ordering. Bonding enthalpies are balanced against entropic tendencies resulting in a rich complicated behavior that leads to clustering that depends on temperature but evolves on picosecond time scales. The structural organization of metallic liquids affects their thermophysical properties, such as viscosity and density, thus influencing the ability of a metallic liquid to form useful technological phases, such as metallic glasses. The time-dependent pair correlation function (the Van Hove function) was determined for metallic-glass forming Cu₄₉Zr₄₅Al₆ at 1060 °C from time-of-flight inelastic neutron scattering measurements made using the Neutron Electrostatic Levitation facility at the Spallation Neutron Source. The time for changes in local atomic connectivity, which is the timescale of atomic ordering, was determined by examining the decay of the nearest neighbor peak. The results of rigorous statistical analyses were used to distinguish between competing models of ordering, suggesting that a stretched exponential model of coordination number change is valid for this system. Full article

Has the mean-variance framework become obsolete? In this paper, we replace traditional variance–covariance methods of portfolio optimisation with relative Tsallis entropy and mutual information measures. Its goal is to enhance risk management and diversification in complicated finance ecosystems. We utilize the S&P 500 and Bitwise 10 cryptocurrency indices’ daily returns (2019–2024 data) and conduct our analysis to the year 2020 under extreme shocks. Many models were trained with different configurations, like mean-variance (MV), mean-entropy (ME), and mean-mutual information (MI) traders and their corresponding variants, using Sharpe’s ratio, Jensen’s alpha, and entropy value of risk (EVAR). The findings indicate that entropic models outperform conventional models in terms of diversification and, especially, extreme risk management. Because the appropriate normalization conditions often fail to be satisfied, we can informally see that after a recalibration of the effective frontier, we obtain from EVAR an accumulated resilience aspect to these rare events while also observing the great potential of entropy-based models to replicate non-linear dependencies between assets. The results show that models combining entropy and mutual information optimise the gain–loss ratio (GLR), providing stable diversification and improved risk management, while maximising returns in complex and volatile market environments. Full article

Background: It is generally accepted that water as a plasticizer can decrease the glass transition temperatures (T_gs) of amorphous drugs and drug delivery systems, resulting in physical instabilities. However, a recent study has reported an anti-plasticizing effect of water on amorphous lidocaine (LID). In co-amorphous systems, LID might be used as a co-former to impair the plasticizing effect of water. Method: Flurbiprofen (FLB) was used to form a co-amorphous system with a mole fraction of LID of 0.8. The effect of water on the stability of co-amorphous FLB-LID upon hydration was investigated. The crystallization behaviors of anhydrous and hydrated co-amorphous FLB-LID systems were measured by an isothermal modulated differential scanning calorimetric (iMDSC) method. The relaxation times of the co-amorphous FLB-LID system upon hydration were measured by a broadband dielectric spectroscopy (BDS), and the differences in Gibbs free energy (ΔG) and entropy (ΔS) between the amorphous and crystalline phases were determined by differential scanning calorimetry (DSC). Results: It was found that the crystallization tendency of co-amorphous FLB-LID decreased with the addition of water. Molecular mobility and thermodynamic factors were both investigated to explain the difference in crystallization tendencies of co-amorphous FLB-LID upon hydration. Conclusions: The results of the study showed that LID could be used as an effective co-former to decrease the crystallization tendency of co-amorphous FLB-LID upon hydration by enhancing the entropic (ΔS) and thermodynamic activation barriers (TΔS)³/ΔG²) to crystallization. Full article

Purpose in systems is considered to be beyond the purview of science since it is thought to be intrinsically personal. However, just as Claude Shannon was able to define an impersonal measure of information, so we formally define the (impersonal) ‘entropic purpose’ of an information system (using the theoretical apparatus of Quantitative Geometrical Thermodynamics) as the line integral of an entropic “purposive” Lagrangian defined in hyperbolic space across the complex temporal plane. We verify that this Lagrangian is well-formed: it has the appropriate variational (Euler-Lagrange) behaviour. We also discuss the teleological characteristics of such variational behaviour (featuring both thermodynamically reversible and irreversible temporal measures), so that a “Principle of Least (entropic) Purpose” can be adduced for any information-producing system. We show that entropic purpose is (approximately) identified with the information created by the system: an empirically measurable quantity. Exploiting the relationship between the entropy production of a system and its energy Hamiltonian, we also show how Landauer’s principle also applies to the creation of information; any purposive system that creates information will also dissipate energy. Finally, we discuss how ‘entropic purpose’ might be applied in artificial intelligence contexts (where degrees of system ‘aliveness’ need to be assessed), and in cybersecurity (where this metric for ‘entropic purpose’ might be exploited to help distinguish between people and bots). Full article

We propose using the ordinal pattern transition (OPT) entropy measured at sentinel central nodes as a potential predictor of explosive transitions to synchronization in networks of various dynamical systems with increasing complexity. Our results demonstrate that the OPT entropic measure surpasses traditional early warning signal (EWS) measures and could be valuable to the tools available for predicting critical transitions. In particular, we investigate networks of diffusively coupled phase oscillators and chaotic Rössler systems. As maps, we consider a neural network of Chialvo maps coupled in star and scale-free configurations. Furthermore, we apply this measure to time series data obtained from a network of electronic circuits operating in the chaotic regime. Full article

This research addresses complexity in manufacturing systems from an entropic perspective for production improvement. The main objective is to develop and validate a methodology that develops an entropic metric of complexity in an integral way in production environments, through simulation and programming techniques. The methodological proposal is composed of six stages: (i) Case study, (ii) Hypothesis formulation, (iii) Discrete event simulation, (iv) Measurement of entropic complexity by applying Shannon’s information theory, (v) Entropy analysis, and (vi) Statistical analysis by ANOVA. The results confirm that factors such as production sequence and product volume significantly influence the structural complexity of the workstations, with station A being less complex (0.4154 to 0.9913 bits) compared to stations B and C, which reached up to 2.2084 bits. This analysis has shown that optimizing production scheduling can reduce bottlenecks and improve system efficiency. Furthermore, the developed methodology, validated in a case study of the metalworking sector, provides a quantitative framework that combines discrete event simulation and robust statistical analysis, offering an effective tool to anticipate and manage complexity in production. In synthesis, this research presents an innovative methodology to measure static and dynamic complexity in manufacturing systems, with practical application to improve efficiency and competitiveness in the industrial sector. Full article