Physical Sciences

Abstract: The isochoric heat capacity of supercritical fluids is a key thermodynamic property for investigating the asymptotic behavior of the Widom line in the vicinity of the critical point. In this wrk, the experimentally determined loci of the isochoric heat capacity maxima along supercritical isotherms are analyzed for a variety of molecular fluids. The experimental results show that the Widom line originates at the critical point, initially shifts toward lower densities with increasing temperature, subsequently reverses direction, and finally approaches the critical density again. Consequently, the Widom line crosses the critical isochore twice. The observed behavior is compared with the predictions of complete and incomplete scaling theories. It is demonstrated that the experimental data are accurately described by the asymptotic relation derived from complete scaling theory, for which the leading coefficient (\(\propto t^{2\beta}\), complete scaling term) is negative, \(D_{\mathrm{CS}} < 0\). This prediction is in excellent agreement with the experimental observations. In contrast, incomplete scaling predicts a different asymptotic behavior (\(\propto t^{1-\alpha}\)) along supercritical isotherms and therefore fails to reproduce the experimentally observed evolution of the Widom line over a wide temperature range. The predictive capability of widely used multiparameter reference equations of state (NIST/REFPROP) is also examined. Although these equations of state accurately represent thermodynamic properties over broad regions of the fluid phase diagram, they fail to reproduce the correct asymptotic behavior of the Widom line in the immediate vicinity of the critical point. This deficiency arises because conventional non-scaling equations of state do not correctly capture the critical anomalies associated with long-range density fluctuations. The present results provide the first experimental confirmation of the asymptotic behavior of the Widom line predicted by complete scaling theory and demonstrate the necessity of incorporating scaling behavior into equations of state intended for accurate description of critical and supercritical fluids thermodynamic behavior.

Abstract: Jaynes’ maximum entropy (MaxEnt) principle selects, from all probability distributions consistent with a set of constraints, the one that maximises the Shannon entropy. The principle is well-defined for classical, real-valued probabilities, but extending it to complex-valued probability theories requires care. Youssef’s complex probability framework, in which quantum mechanics is reformulated as a Bayesian theory with complex amplitudes and the observable probability is the squared modulus (Born rule), does not admit a natural MaxEnt extension: the L² normalization of that framework is incompatible with the L¹ normalization assumed by Shannon entropy, and the resulting complex-valued entropy functional cannot be maximized without additional structure absent from Youssef’s axioms. The present paper proposes a different extension of Kolmogorov’s axioms to the complex domain, replacing non-negativity with the condition that the real part of every probability be non-negative. This framework, which retains L¹ normalization and recovers classical probability when the imaginary part vanishes, admits a natural MaxEnt principle: the real part of the complex Shannon entropy is a well-posed real functional, its Euler–Lagrange equations produce an explicit complex Gibbs distribution with complex Lagrange multipliers, and the classical Gibbs distribution is recovered as the special case of real multipliers. The die problem (Jaynes’ Brandeis dice example) is worked out in detail for both the fair and the loaded cases, illustrating how imaginary constraints redistribute the observable probability mass in a way that has no counterpart in classical MaxEnt.

Abstract: To address the energy conversion and entropy change during the thermoelastic effect, the first and second laws of thermodynamics are applied in the coupled thermal and elastic fields in this paper to analyze these two issues. The underlying physical mechanism for energy conversion is explained in details and the specific term which is responsible for energy conversion between the two coupled fields is also identified explicitly. As a result, the governing equations which directly satisfy the law of conservation of energy are determined for both the elastic and thermal fields. Moreover, variation of the total entropy during the thermoelastic effect within the considered system is also analyzed. Both the contributions to the entropy change at the surface and within the bulk of the system are obtained with straightforward physical contents. In the end, a preliminary discussion on the thermoelastic effect under thermal shock is also presented. The governing equations for both fields are also obtained with the one for the thermal field being a wave-type equation.

Abstract: We present a comprehensive theoretical and computational formulation of the Dead Universe Theory (DUT), a thermodynamic theory of gravitation in which the observed late-time cosmic acceleration, the suppression of large-scale structure growth, and the background expansion emerge from irreversible entropic gravitational dynamics rather than from a positive cosmological constant. Starting from the DUT action, we derive the corresponding autonomous cosmological system and its perturbative sector, demonstrating that the cosmological growth index is a theoretical prediction rather than an observationally calibrated quantity. The asymptotic perturbative dynamics leads uniquely to the characteristic equation γ² + γ − 1 = 0, yielding the fixed solution γ = (√5 − 1)/2 ≈ 0.6180339887 without phenomenological fitting or adjustable parameters.The theoretical framework is implemented through three independent scientific software platforms developed by ExtractoDAO Labs: the TON618 RK4 Engine, the DUT Calibration Engine, and the DUT CMB Scientific Engine. Together, these independent implementations provide computational verification of the theoretical predictions and enable a unified comparison with measurements of the local Hubble constant, the growth-rate observable fσ₈, Pantheon+ Type Ia supernovae, baryon acoustic oscillations, and Planck 2018 CMB distance priors.The DUT framework predicts H₀(local) = 73.88 km s⁻¹ Mpc⁻¹, H₀(CMB) = 67.39 km s⁻¹ Mpc⁻¹, w_eff(z = 0) = −0.9918, and fσ₈(z = 0) = 0.4224. Relative to the reference ΛCDM cosmology, the present implementation yields improvements of Δχ² = −41.09 in the growth sector, Δχ² = −28.76 for the local Hubble constraint, and Δχ² = −211.60 for the combined Pantheon+, BAO, and Planck 2018 CMB distance-prior analysis, corresponding to an overall improvement of Δχ² = −281.45 under the observational datasets analyzed in this work.The DUT framework predicts a unique, fixed value of the cosmological growth index, γA = (√5 − 1)/2 ≈ 0.6180339887, where γA denotes the DUT growth index. This prediction is fully falsifiable: a statistically significant and reproducible measurement inconsistent with γA = 0.6180339887 would refute the perturbative DUT framework without introducing additional parameters or phenomenological recalibration. Unlike cosmological frameworks whose growth predictions are obtained through parameter estimation within a global fit, the DUT prediction constitutes an a priori theoretical result derived directly from first principles. The DUT growth index therefore establishes a quantitative observational benchmark against which competing cosmological theories can be objectively tested.

Abstract: A general model of superconductivity mechanism based on the separation of overlapping subbands near the Fermi level in highly degenerate materials is presented. Despite some unconventional properties, high-temperature superconductors exhibit fundamental behaviors common to low-temperature superconductors. In accordance with Fermi-Dirac statistics, the Landau-Ginzburg second-order phase transition and thermodynamic relations for superconductors, the fundamental characteristics, such as the Gibbs free energy, the total system energy, the electron density of states, the energy gap, and the entropy dependences on temperature are presented. It is shown that a main error in the BCS model is the concept that any free electron passing through the lattice polarizes the lattice ions along its path, because almost all metal atoms are neutral. Below the energy gap, there are no separate electrons; free randomly moving electrons are only above the energy gap. The proposed model is applicable to both low- and high-temperature superconductors. It is shown that the main thermodynamic equations describe both the normal and superconducting phases: the free energy, the total electron energy, the energy gap, and the entropy of a highly degenerate electron gas.

Abstract: It is shown that the Clausius entropy is additive under certain conditions. It is suggested that these conditions are fulfilled for a not too large composite of disjoint, adjacent thermodynamic systems existing contemporaneously, and without relative speed. The point of view is the macroscopic and nonstatistical one of classical thermodynamics.

Abstract: This paper assumes that a thermodynamic system can be composed purely of coherence and information, and constructs a working model on that basis. We derive operational parameters for such systems using definitions of the Certainty Equation, semantic entropy, semantic temperature, and formulate five laws and three modes of coherence and information systems. This analysis is then compared to the features of black holes.

Abstract: Generative artificial intelligence is increasingly embedded in recursive informational ecosystems in which outputs are produced, published, retrieved, summarized, copied and pasted into new human or machine production. This paper proposes a preliminary predictive framework for Dissipative Semantic Homogenization (DSH), a possible re-gime in which recursive generative AI ecosystems dissipate physical energy while corpus-level semantic diversity contracts and saturates. The framework does not iden-tify thermodynamic entropy with semantic entropy. Instead, it treats them as opera-tionally coupled variables: semantic distributions are transformed by physically im-plemented computation, while energy dissipation provides a macroscopic cost proxy. We model semantic diversity as Shannon entropy over a corpus-level partition of se-mantic states and introduce modal amplification, independent novelty injection, and AI assimilation of nominally human production as control variables. The model yields empirically testable implications: semantic contraction should occur only when effec-tive independent novelty falls below a stability threshold; contraction should be scale-dependent; and cumulative semantic loss should saturate even while physical entropy production continues. The framework is not presented as an empirical law, but as a testable theoretical model for future longitudinal and controlled studies.

Abstract: It is shown that the Clausius entropy and the internal energy can be taken to be additive for systems existing next to each other, contemporaneously, and without relative speed. Also, it is shown that any thermodynamic state quantity is extensive if it is additive and if its volume density is finite. It is argued that for many state quantities the assumption of extensivity can be replaced by the assumption of finite density. The point of view is the macroscopic and non-statistical one of classical thermodynamics.

Abstract: The Gibbs Paradox (concerning the entropy of mixing and entropic extensivity) was explored in depth by Edwin Jaynes (1992). We take up Jaynes’ treatment, considering the special cases for which entropy is (approximately) extensive, and the general case in which it is not. We also explore the Holographic Principle which (strictly speaking) excludes the extensivity of entropy. The formalism of Quantitative Geometrical Thermodynamics shows that, being isomorphic to energy, it is entropy production (not entropy) that is extensive. As a corollary, Shannon information is also not extensive, although information production is extensive.

Abstract: Upper troposphere (UT) humidity records are crucial for climate studies. Pseudo-monthly averaging limited just to nighttime measurement is applied to maximize temporal representativeness and enhance the lidar signal, providing WVMR profiles up to 16 km. This study evaluates 11 years (2013–2023) of water vapor mixing ratio (WVMR) profiles from a UV Raman lidar (Lid1200) at Réunion Island against MLS-Aura satellite retrieval, ERA5 reanalysis, and GRUAN-processed M10 radiosondes. The results show a systematic dry shift in MLS of up to 30% above 12 km, particularly during the wet season. Lidar exhibits a slight downward shift in WVMR, around 5% lower than ERA5 throughout the UT, with the largest deviations present above 14 km and greater variability during the wet season, Lidar calibration-related challenges during the dry season result in drier-than-ERA5 WVMR profiles (up to 10%). Additionally, comparisons with GRUAN-processed radiosonde reveal a substantial dry shift relative to the lidar, exceeding 30% above 12 km. We investigate the GNSS-based lidar calibration effect by applying an alternative calibration method. This produces higher WVMR values, revealing an ERA5 dry shift relative to lidar, increasing with altitude at the UT up to 25%. These measurements complement the global effort in monitoring and validating the tropical and subtropical upper tropospheric humidity.

Abstract: A nano-porous tubular ceramic membrane(TCM) is developed to recover water vapor and its significant amount of latent heat from flue gas to save water and reduce the acid dew point. The experimental and numerical investigation on both normal condensation(NCD) and capillary condensation(CCD) by insetting a horizontal TCM into membrane module. By taking user defined function(UDF) of Fluent14.5, source terms of governing equations are conducted to illuminate the NCD, capillary condensation and effects of the inertia force(F_i) on heat and mass transfer. Several cases with feed gas inlet velocity(U_in), mass fraction of non-condensable gas (W_con), cooling water inlet temperature(T_cool) and time steps(t) are simulated, and the errors between experimental and numerical results are less than 1.14%. The results show that the thermal performance of TCM in the NCD is more significant than which in the CCD. The NCD proceeds significantly during flow in the TCM, while the CCD proceeds mainly in the backside of TCM(x-coordinate is larger than 500mm nearly). The U_in, W_con and T_cool have a remarkable effect on thermal and mass-transfer characteristics.

Abstract: The entropy of a Schwarzschild black hole is commonly derived using thermodynamic relations whose physical interpretation is not always transparent, in particular with re-spect to the localization of temperature and entropy. In this paper, we present a derivation of the Bekenstein–Hawking entropy based exclusively on the principles of phenome-nological thermodynamics, formulated entirely in regions where spacetime is effectively flat. The analysis considers a reversible evaporation process in which the black hole is sur-rounded by a tunable thermal radiation bath whose temperature is kept arbitrarily close to the Hawking temperature. In this limit, entropy production can be made negligible. By integrating the entropy flux through a distant reference surface over the evaporation process, the standard entropy formula is obtained without invoking assumptions about the localization of the black hole entropy or about microscopic degrees of freedom. The derivation is mathematically simple but conceptually instructive. The approach is intended to be accessible to readers familiar with classical thermodynamics and general relativity at an advanced undergraduate or graduate level.

Abstract: In the introduction, a brief history of the body selection that would define the inertial frame of reference in mechanics (and electrodynamics) is given. At the same time, attention has been drawn to Einstein's opinion about the (unrealized) causal relationship which should exist between the frame of reference and the law that is formulated from it. Therefore, parts 2 to 5 gradually present and elaborate the idea that, instead of directly choosing a body of reference, the criterion which will give legitimacy to the selection result should be defined first. And the criterion is such that the reference body is ensured by causality just mentioned by Einstein. Such a criterion for the fields of mechanics and thermodynamics is defined here and called the "criterion of observer's non-involvement in the observed” by a reference body. In the conclusion, as the main result, significant changes in the formulations of mechanics and thermodynamics, which the application of the criterion leads to, are stated. In those improved formulations the contents related to the observer are separated from the contents related to laws of nature.

Abstract: Metabolism in living things is the combination of enzyme-catalyzed biochemical reactions that drive biological work in the form of energy capture and release, molecule synthesis, cell replication and other functions. It is constrained by many factors, including resources, enzyme characteristics, and temperature under the requirement that organisms persist through time. Here, the biochemical foundation for metabolism is viewed from a thermodynamic perspective that explores three different metabolic currencies: (1) entropy production, which reflects the ability to persist at or near steady state through time by the rate at which entropy of surroundings is increased relative to that inside a system, (2) reaction rate or the rate of formation of products, and (3) power, the rate at which “free” (Gibbs) energy available for doing work is generated. Rate-temperature relationships for each objective are derived from a reaction-displacement model of a metabolic reaction for near-steady-state conditions, which are presumed to be required for organisms to persist over time. Reaction rate, entropy production and Gibbs energy production are maximized at different optimal temperatures, T_opt, all at barely distinguishable near-maximum reaction rates. These theoretical predictions nevertheless provide distinct, testable hypotheses for organism response to temperature under maximizing each of the three metabolic currencies. The framework also suggests that there exists a maximum temperature for life, T_max, at which entropy generated near reaction sites by reaction activation becomes greater than that generated away from reaction sites by the dissipation of heat and products. The framework predicts shifts in Topt and T_max that differ among types of reactions, enzyme concentrations, organism element concentration and varying body size. Overall, the framework provides a greatly expanded set of hypotheses and explanations for temperature performance relationships for life, including variation in both T_opt and T_max, for growth versus locomotion and respiration, “fast” versus “slow” life histories, resource-rich versus resource-poor environments, and intra- and interspecific variation in body size.

Abstract: This paper presents a practical implementation of relative primary radiation thermometry (RPRT) together with MultiFixRadSoft, an open-source software package developed in accordance with the Mise-en-Pratique for the kelvin (MeP-K) for realization of the thermodynamic temperature scale and uncertainty evaluation under the new definition of the kelvin. The software enables realization of temperature scales using ITS-90 metal fixed points as well as metal–carbon and metal–carbide–carbon eutectic high-temperature fixed points (HTFPs) for both radiation thermometers and radiometers. It incorporates automated routines for melting-plateau analysis, including determination of the point of inflection, liquidus point, and melting range, together with correction modules for size-of-source effect, detector nonlinearity, emissivity, and temperature-drop. Validation is demonstrated through experimental realization using six fixed points (Cu, Fe–C, Co–C, Pd–C, Ru–C, and WC–C) and a linear radiation thermometer. The software also supports ITS-90 extrapolation procedures and flexible calibration schemes (n = 1 to n ≥ 3), with automated Sakuma–Hattori fitting and full uncertainty propagation compliant with MeP-K requirements. Results show excellent agreement with manual analyses and published data, confirming the correctness of the implemented algorithms. By integrating data processing, scale realization, and uncertainty analysis within a unified and transparent framework, MultiFixRadSoft provides a robust and accessible tool for traceable radiometric thermometry, supporting emerging NMIs and industrial laboratories while promoting wider adoption of primary thermodynamic temperature realization methods.

Abstract: Redefining of the notions of econophysics based on the Landauer principle is suggested. Economic temperature is defined via the economic Landauer principle. The economic temperature is proportional to the minimal monetary cost associated with erasing or transmitting one bit of information in a given economic system. The introduced definition is useful for high-frequency trading. Clausius formulation of the Second Law of Thermodynamics for economic systems is formulated as follows: energy/money cannot spontaneously flow from a colder economic system to a hotter economic system. Carnot and Szilard’s economical engines are addressed. The Carathéodory formulation of the Second Law of Thermodynamics is re-shaped as follows: in every neighborhood of any equilibrium economic state, there exist states that cannot be reached by the process, which does not spend money or information. Optimal-power Curzon–Ahlborn economic engine is discussed.

Abstract: The burning candle discussed in Faraday's lectures is used as an example to discuss the relationships between physical theories at different levels of organization: continuum mechanics at the macro level and statistical and quantum mechanics at the micro level. The first part of the paper examines the connections between theoretical and experimental physics. Physics theory serves as the foundation of the research program, but experimental research is a measure of ongoing development. Reasonable extrapolationism denotes a situation where the ideas of physical theory contribute to the development of experimental research. On the other hand, radical extrapolationism is used for a situation where the ongoing discussion goes far beyond experimental physics. In the second part of the paper, the arrows of explanation between continuum mechanics and statistical mechanics are considered and classified within the framework of the proposed terminology. The estimation of the properties of a substance from molecular constants and the derivation of continuum mechanics equations from statistical mechanics are considered. Qualitative explanations and emergence are also discussed.

Abstract: We propose a thermodynamic variational framework in which quantum mechanics, classical dynamics, and gravitation emerge as equilibrium regimes of a single free-energy functional defined on probability distributions rather than on trajectories, wavefunctions, or spacetime metrics. The functional balances Fisher information, potential energy, and Shannon entropy, encoding an exploration–exploitation trade-off uniquely fixed by information-theoretic considerations. Matching the Fisher term to the quantum kinetic energy fixes its coefficient without free parameters. Extremization of the functional yields the continuity equation and the quantum Hamilton–Jacobi equation, and thus reproduces the Schrödinger equation as a thermodynamic equilibrium condition. At mesoscopic scales, competition between Fisher information and entropy introduces a characteristic quantum–classical crossover length that provides a thermodynamic perspective on decoherence. Measurement is interpreted as an irreversible thermodynamic transition, with energetic costs bounded by Landauer's principle. In the macroscopic regime, we show that requiring thermodynamic stability and local boundary response selects area-law entropy scaling as the leading contribution under stated assumptions. Given an area-law entropy, standard local arguments recover Einstein's field equations. The framework yields falsifiable predictions across quantum, mesoscopic, and gravitational regimes.

Abstract: Area-law entropy appears in quantum many-body systems and gravitational physics, whereas classical thermodynamics treats entropy as volume-extensive. Rather than reflecting competing fundamental principles, we show that these scalings correspond to distinct thermodynamic stability regimes. Using a minimal information-theoretic free-energy functional combining Fisher information and Shannon entropy, we analyze entropy scaling under three physically unavoidable requirements: locality of response, existence of thermodynamic equilibrium, and universality of gravitational coupling. Within this framework, we prove that volume-law entropy cannot define an intrinsically stable equilibrium for isolated macroscopic systems and is therefore viable only as an externally stabilized, mesoscopic approximation. We identify three regimes. At microscopic scales, Fisher dominance and locality of information propagation enforce area-law entropy. At intermediate scales, volume-law entropy emerges as a metastable regime sustained by non-gravitational confinement. At macroscopic scales dominated by self-gravity, we show that thermodynamic stability and composition-independent equilibrium uniquely require area-law entropy; any more extensive scaling leads either to instability or to violations of the equivalence principle. Volume-law entropy is thus identified as a mesoscopic anomaly rather than a fundamental property of matter. Area-law scaling emerges as the only entropy behavior consistent with a unified thermodynamic description spanning quantum coherence and gravitational universality.