Physical Sciences

Abstract: Here, we have shown that the temperature \((T)\) of an inert gas is proportional to \(w^{\frac{k_B}{nC_p}}\), where \(w\) is the number of microstates, \(n\) is the number of moles and \(C_p\) is the molar heat capacity at constant pressure and \(k_B\) is the Boltzmann constant. The above relationship has been found to be valid using experimental data in a wide range of temperature, e.g., \([298\,\mathrm{K}\text{--}6{,}000\,\mathrm{K}]\) for all the inert gases and we have documented their respective proportionality constants. On the other hand, for the non-inert gases, we have shown that the number of microstates is proportional to \[ T^{nA/k_B} \times e^{\frac{nBT}{1000k_B} + \frac{nCT^2}{2\times 1000^2\times k_B} + \frac{nDT^3}{3\times 1000^3\times k_B} - \frac{nE\times 1000^2}{T^2\times k_B}}, \] where \(A, B, C, D, E\) are coefficients of the Shomate equation for molar heat capacity at constant pressure. For three non-inert gases, namely, Hydrogen, Nitrogen and Oxygen, here we have estimated the values of the respective proportionality constants as well.

Abstract: The article is a continuation of research on the status and formulations of the second law of thermodynamics. In the first paper of this series, it was shown that the Kelvin formulation and the temperature formulation of Clausius are not exhaustive compared to the entropy formulation and the generalized Carnot-type formulation. In the previous paper, it was furthermore shown that the statistical formulation is even more problematic. This has now been supported with quotes from Smoluchowski in contrast to quotes from Eddington. A probabilistic scheme (now refined as a combinatorial one) for the second law of thermodynamics was previously proposed, which is not burdened by a fundamental/non-emergent arrow of time and the Loschmidt reversibility paradox. The present new paper numerically investigates and visualizes the combinatorial scheme for the 12 smallest systems of spheres in cells (including 10 equinumerous cases). Despite the small number of balls (from 2 to 11), the number of macrostates in the last system reaches a value of 356 716, with the number of microstates equal to 285 311 670 611. The combinatorial scheme is additionally expanded by three criteria/properties of emergence: cumulative, cardinal, and probabilistic. The first two properties, cumulative and cardinal, of emergence are confirmed (at least in the equinumerous cases), and halfway probabilistic emergence 50%-50% is postulated as an asymptotic hypothesis for larger systems.

Abstract: This paper reinterprets the mechanics of projectile motion with quadratic aerodynamic drag through the lens of non-equilibrium thermodynamics and information theory. Rather than treating aerodynamic drag merely as mechanical energy loss, we develop dual augmented Lagrangians (L_S^* and L_I^*) that unify macroscopic energy and entropy balances within a single variational framework. By reformulating the system in both thermodynamic and purely informational terms, a conceptual duality is established. The resulting variational saddle-point represents a dynamic compromise: it balances the natural drive to rapidly erase the system's initial kinematic state against the intrinsic mechanical and thermodynamic inertia that resists instantaneous dissipation. Applying this framework, analytical results reveal that the classical bounded parabolic flight is fundamentally an incomplete thermodynamic transient. Entropy production is non-homogeneous throughout the trajectory, as we find that the optimal launch angle for maximum horizontal range does not correspond to a global thermodynamic extremum. Instead, this geometric optimum is a parametric artefact forced by the ground impact, which arbitrarily truncates the system's natural phase-space evolution toward its steady-state attractor, the terminal velocity. Ultimately, this framework proves that the continuous phase-space contraction and erasure of macroscopic kinematic information imposes an unavoidable cubic thermodynamic tax on the environment. By explicitly correlating mechanical dissipation with informational loss, we establish a firm macroscopic connection between classical mechanics, non-equilibrium thermodynamics, and the physics of information.

Abstract: In this paper, the first and second laws of thermodynamics are applied in the coupled thermal and elastic fields to analyze the energy conversion and entropy change during the thermoelastic effect. The underlying physical mechanism for energy conversion is explained and the specific term which is responsible for energy conversion between the two coupled fields is also identified. As a result, 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 is also analyzed. Both 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; governing equations for both fields are also obtained with that for the thermal field being a wave-type equation.

Abstract: The goal of this work is simple and traditional: to provide a formalization and generalization of the notion of entropy in the spirit of Carnot. The tools we employ to achieve our objective are quite novel however. We have no need for state spaces, paths in state spaces, path integration,cycles in state spaces, systems in equilibrium, quasi-static transformations, the usual dynamical notion of reversibility, or even, the first law of thermodynamics. Instead, we rely on a primitive notion of process and the effects a process has on a system, typically, on the surroundings of a system. Carnot cycles are replaced in our framework by bithermal processes. We recover that the efficiency of a bithermal process is maximal when the process is reversible and maximal efficiency is determined by the temperature of the reservoirs. We also derive that all cyclic processes are dissipative, at best isentropic. The formalism assigns a degree of irreversibility to every process. The argument we present is quite general. It does not assume systems to be at equilibrium; it simply requires systems to have a state at the beginning and at the end of the process.

Abstract: It is well-known that Shannon information may be represented in the usual formalism by points of non-analyticity. We show (assuming that the Second Law of Thermodynamics is taken as axiomatic) that it may also be generated by recursive systems. Trajectories of causality across complex time entail the generation of Shannon information (“entropic purpose”) while recursively causal trajectories also entail the complexification of probability. Causal trajectories across the complex temporal plane, while preserving the distinction between cause and effect (in accordance with the Second Law), also underpin the coherent interplay between the physical effects of acausal Shannon information and purposive agents of causation.

Abstract: Nanothermodynamics describes the process where large systems subdivide into equilibrium distributions of small subsystems. A key ingredient is Hill’s subdivision potential (E) that ensures adherence to the 1st and 2nd laws of thermodynamics in systems of any size. In this review and reassessment, it is emphasized that nanothermodynamics gives new insight into many measurements, theories, and simulations. Measurements establishing the need for nanothermodynamics show thermodynamic heterogeneity from multiple effective temperatures (Ti) inside most types of materials. One theoretical result that requires E=0 is the stable solution of Ising’s original model for finite chains of interacting spins, a solution Ising could not have found 40 years before Hill’s work. Another result is a novel solution to Gibbs’ paradox that makes the entropy of the semiclassical ideal gas exactly extensive. Molecular dynamics simulations reveal how a standard fluctuation relation is modified when local degrees of freedom fluctuate faster than their coupling to the heat bath, consistent with the measured thermodynamic heterogeneity. Simulations of a Creutz-like model, comprised of Ising spins coupled to an explicit heat bath of Einstein oscillators, are used to study the 2nd law. It is found that maximizing the total entropy (St) requires an intrinsically irreversible step, providing a counterexample to the usual claim that statistical mechanics emerges from reversible dynamics. Furthermore, fluctuations of this model are best described by Einstein’s reversal of Boltzmann’s relation and the 2nd-law, not by recent fluctuation theorems.

Abstract: Driven by the common entropy formalism in statistical physics and information theory here we show that methods developed for the analysis of molecular conformational ensembles may be successfully used for classification. Entropy is estimated using the k-th nearest neighbour method combined with the Maximum Information Spanning Tree method to account for the mutual informations between variables. This formalism is used to classify new samples using their estimated cross-entropy with the training set. The method is tested using diverse datasets and the results obtained are comparable to those obtained by machine learning methods, or better when the number of samples is small. The methods described here have the advantage, compared to other classification methods, of directly linking variables and pairs of variables to the assigned class, a valuable feature when aiming at identifying causative relationships between features and classes (e.g. the relationship between genes and diseases).

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: 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.