Search Results (855)

In this paper, we introduce Kluitenberg’s formulation of non-equilibrium thermodynamics with internal variables in the context of a Riemannian space, as required by Einstein’s general relativity. Using the formulation of the second law of thermodynamics in general coordinates with a pseudo-Euclidean metric, we derive a Levi-Civita-like energy tensor and propose a generalization of the second law within a Riemannian space, in agreement with Tolman’s approach. In addition, we determine the expression for the entropy density in a general Riemannian space and identify the new variables upon which it depends. This allows us to deduce, within this framework, the equilibrium inelastic and viscous stress tensors as well as the entropy production. These expressions are consistent with the principle of general covariance and Einstein’s equivalence principle. Full article

We investigate the statistical entropy of black holes within the framework of the generalized uncertainty principle (GUP) by employing effective metrics that incorporate leading-order and all-order quantum gravitational corrections. We construct three distinct effective metrics induced by the GUP, which are derived from the GUP-corrected temperature, entropy, and all-order GUP corrections, and analyze their impact on black hole entropy using ’t Hooft’s brick wall method. Our results show that, despite the differences in the effective metrics and the corresponding ultraviolet cutoffs, the statistical entropy consistently satisfies the Bekenstein–Hawking area law when expressed in terms of an invariant (coordinate-independent) distance near the horizon. Furthermore, we demonstrate that the GUP naturally regularizes the ultraviolet divergence in the density of states, eliminating the need for artificial cutoffs and yielding finite entropy even when counting quantum states only in the vicinity of the event horizon. These findings highlight the universality and robustness of the area law under GUP modifications and provide new insights into the interplay between quantum gravity effects and black hole thermodynamics. Full article

Classical thermodynamics omits rigidity, which property distinguishes solids from gases and liquids. By accounting for rigidity (i.e., Young’s elastic modulus, ϒ), we recently amended historical formulae and moreover linked heat capacity, thermal expansivity, and ϒ. Further exploration is motivation by the importance of classical thermodynamics to various applied sciences. Based on heat performing work, we show here, theoretically, that density times sublimation enthalpy divided by the molar mass (ρΔH_sub/M, energy per volume), depends linearly on ϒ (1 GPa = 10⁹ J m⁻³). Data on diverse metals, non-metallic elements, chalcogenides, simple oxides, alkali halides, and fluorides with cubic structures validate this relationship at ambient conditions. Furthermore, data on hcp metals and molecular solids show that ρΔH_sub/M is proportional to ϒ for anisotropic materials. Proportionality constants vary only from 0.1 to 0.7 among these different material types (>100 substances), which shows that the elastic energy reservoir of solids is large. Proportionality constants depend on whether molecules or atoms are sublimated and are somewhat affected by structure. We show that ductility of refractory, high-ϒ metals affect high-temperature determinations of their ΔH_sub. Our results provide information on sublimation processes and subsequent gas phase reactions, while showing that elasticity of solids is the key parameter needed to assessing their energetics. Implications are highlighted. Full article

We present a thermodynamically consistent energetic variational model for active nematics driven by ATP hydrolysis. Extending the classical Toner–Tu framework, we introduce a chemo-mechanical coupling mechanism in which the self-advection and polarization dynamics are modulated by the ATP hydrolysis rate. The model is derived using an energetic variational approach that integrates both chemical free energy and mechanical energy into a unified energy dissipation law. The reaction rate equation explicitly incorporates mechanical feedback, revealing how active transport and alignment interactions influence chemical fluxes and vice versa. This formulation not only preserves consistency with non-equilibrium thermodynamics but also provides a transparent pathway for modeling energy transduction in active systems. We also present numerical simulations demonstrating the positive energy transduction under a specific choice of model parameters. The new modeling framework offers new insights into energy transduction and regulation mechanisms in biologically related active systems. Full article

Thermodynamic simulations of fluid–rock interactions provide valuable insights into mineral deposit formation mechanisms. This study investigates the Pulang porphyry Cu-Au deposit in the Sanjiang Tethys Orogen, employing both Gibbs energy minimization (GEM) and the Law of mass action (LMA) method to understand alteration overprinting and metal precipitation. The modeling results suggest that the ore-forming fluid related to potassic alteration was initially oxidized (ΔFMQ = +3.54~+3.26) with a near-neutral pH (pH = 5.0~7.0). Continued fluid–rock interactions, combined with the input of reduced groundwater, resulted in a decrease in both pH (4.8~6.1) and redox potential (ΔFMQ~+1), leading to the precipitation of propylitic alteration minerals and pyrrhotite. As temperature further decreased, fluids associated with phyllic alteration showed a slight increase in pH (5.8~6.0) and redox potential (ΔFMQ = +2). The intense superposition of propylitic and phyllic alteration on the potassic alteration zone is attributed to the rapid temperature decline in the magmatic–hydrothermal system, triggering fluid collapse and reflux. Mo, mainly transported as HMoO₄⁻ and MoO₄⁻², precipitated in the high-temperature range; Cu, carried primarily by CuCl complexes (CuCl₄⁻³, CuCl₂⁻, CuCl), precipitated over intermediate to high temperatures; and Au, transported as Au-S complexes (Au(HS)₂⁻, AuHS), precipitated from intermediate to low temperatures. This study demonstrates that fluid–rock interactions alone can account for the observed sequence of alteration and mineralization in porphyry systems. Full article

The symmetry of the interparticle interaction potential (IIP) plays a critical role in determining the thermodynamic and transport properties of solids. This study investigates the isolated effect of IIP asymmetry on thermalization. Asymmetry and nonlinearity are typically intertwined. To isolate the effect of asymmetry, we introduce a one-dimensional asymmetric harmonic (AH) model whose IIP possesses asymmetry but no nonlinearity, evidenced by energy-independent vibrational frequencies. Extensive numerical simulations confirm a power-law relationship between thermalization time (T_eq) and perturbation strength for the AH chain, revealing an exponent larger than the previously observed inverse-square law in the thermodynamic limit. Upon adding symmetric quartic nonlinearity into the AH model, we systematically study thermalization under combined asymmetry and nonlinearity. Matthiessen’s rule provides a good estimate of T_eq in this case. Our results demonstrate that asymmetry plays a distinct role in enhancing higher-order effects and governing relaxation dynamics. Full article

The Polish Free-Electron Laser (PolFEL), which is currently under construction in the National Centre for Nuclear Research in Świerk near Warsaw, will comprise an electron gun and from four to six cryomodules, each accommodating two nine-cell TESLA RF superconducting resonant cavities. To cool the superconducting resonant cavities, the cryomodules will be supplied with superfluid helium at a temperature of 2 K. Other requirements regarding the cooling power of PolFEL result from the need to cool the power couplers for the accelerating cryomodules (5 K) and thermal shields, which limit the heat inleaks due to radiation (40–80 K). The machine will utilize several thermodynamic states of helium, including two-phase superfluid helium, supercritical helium, and low-pressure helium vapours. Supercritical helium will be supplied from a cryoplant by a cryogenic distribution system (CDS)—transfer line and valve boxes—where it will be thermodynamically transformed into a superfluid state. This article presents the architecture of the CDS, discusses several design solutions that could have been decided on with the use of second law analysis, and presents the design methodology of the chosen CDS elements. Full article

Our study lies at the intersection of three fields: finite-time thermodynamics, relativity theory, and the theory of hyperbolic conservation laws. Each of these fields has its own requirements and richness, and in order to link them together as effectively as possible, we have simplified each one, reducing it to its fundamental principles. The example chosen concerns the propagation of chemical changes in a very large reactor, as found in geology. We ask ourselves two sets of questions: (1) How do the finiteness of propagation speeds modeled by hyperbolic problems (diffusion is neglected) and the finiteness of the time allocated to transformations interact? (2) How do the finiteness of time and that of resources interact? The similarity in the behavior of the pairs of variables (x, t and resources, resource flows) in Lorentz relativistic transformations allows us to put them on the same level and propose complementary-type relationships between the two classes of finiteness. If times are finite, so are resources, which can be neither zero nor infinite. In hyperbolic problems, a condition is necessary to select solutions with a physical sense among the multiplicity of weak solutions: this is given by the entropy production, which is Lorentz invariant (and not entropy alone). Full article

Thermodynamic systems admit multiple equivalent descriptions related by transformations that preserve their fundamental structure. This work focuses on exact isohomogeneous transformations (EITs), a class of mappings that keep fixed the set of independent variables of the thermodynamic potential, while preserving both the original homogeneity and the validity of a first law. Our investigation explores EITs within the extended Iyer–Wald formalism for theories containing free parameters (e.g., the cosmological constant). EITs provide a unifying framework for reconciling the diverse formulations of Kerr-anti de Sitter (KadS) thermodynamics found in the literature. While the Iyer–Wald formalism is a powerful tool for deriving first laws for black holes, it typically yields a non-integrable mass variation that prevents its identification as a proper thermodynamic potential. To address this issue, we investigate an extended Iyer–Wald formalism where mass and thermodynamic volume become gauge dependent. Within this framework, we identify the gauge choices and Killing vector normalizations that are compatible with EITs, ensuring consistent first laws. As a key application, we demonstrate how conventional KadS thermodynamics emerges as a special case of our generalized approach. Full article

We investigate the evolution of future trapping horizons through the dynamics of the Misner–Sharp mass using ingoing Eddington–Finkelstein coordinates. Our analysis shows that an integral formulation of Hayward’s first law governs much of the evolution of general spherically symmetric spacetimes. To account for the accretion backreaction, we consider a near-horizon approximation, which yields first-order corrections of a Vaidya-dark energy form. We further propose a systematic perturbative scheme to study these effects for an arbitrary background. As an application, we analyze an accreting Reissner–Nordström black hole and demonstrate the horizon shifts produced. Finally, we compute accretion-induced corrections to an extremal configuration. It is shown that momentum influx and energy density produce distinct effects: the former forces the splitting of the extremal horizon, while the latter induces significant displacements in its position, computed up to first-order perturbative corrections. These results highlight how different components of the stress–energy tensor significantly affect horizon geometry, with potential implications for broader areas of research, including black-hole thermodynamics. Full article

McComas et al. (2025) introduced a numerical experiment, where ordinary uncorrelated collisions between collision pairs are followed by other, controlled (correlated) collisions, shedding light on the emergence of kappa distributions through particle correlations in space plasmas. We extend this experiment by introducing correlations indicating that (i) when long-range correlations are interwoven with collision pairs, the resulting thermodynamic kappa are described as that corresponding to an ‘interatomic’ potential interaction among particles; (ii) searching for a closer description of heliospheric plasmas, we found that pairwise short-range correlations are sufficient to lead to appropriate values of thermodynamic kappa, especially when forming correlated clusters; (iii) multi-particle correlations do not lead to physical stationary states; finally, (iv) an optimal model arises when combining all previous findings. In an excellent match with space plasmas observations, the thermodynamic kappa that describes the stationary state at which the system is stabilized behaves as follows: (a) When correlations are turned off, kappa is turning toward infinity, indicating the state of classical thermal equilibrium (Maxwell-Boltzmann distribution), (b) When collisions are turned off, kappa is turning toward the anti-equilibrium state, the furthest state from the classical thermal equilibrium (−5 power-law phase-space distribution), and (c) the finite kappa values are generally determined by the competing factor of collisions and correlations. Full article

Based on the First and the Second laws of Thermodynamics the energy dissipated in engineering materials and structures is calculated in a multidimensional mechanics framework. The existing practice of computing the dissipated energy by the area of the stress-strain (or force-displacement) curve is objected to. The conditions under which the area of a stress-strain diagram correctly measures the dissipated energy are derived and clearly presented. A general mathematical form for the dissipated energy when those conditions are not satisfied is provided. An internal variables formulation is employed in this work. Erroneous results from the literature calculating the dissipated energy are given. Erroneous calculations are abundant in publications, Theses and Dissertations, books, and even engineering codes. The terms hysteresis and hysteretic loss are technically explained and their wrong use in cases other than in viscoelasticity is explicated. Full article

The paper considers an extended interpretation of the second law of thermodynamics and its implications to power conversion optimization in multidomain systems. First, a generalized, domain-independent version of the classical Gouy-Stodola theorem is derived for interconnected systems which satisfy the Clausius postulate of the second law. Mechanical, electrical and more general Hamiltonian systems do not satisfy this postulate, however the related property of energy cyclodirectionality may be satisfied. A generalized version of the Gouy-Stodola theorem is then obtained in inequality form for systems satisfying this property. The result defines average forms of entropy generation and lost work for multi-domain systems. The paper then formulates an optimal control problem for a representative electromechanical system, obtaining complete, closed-form solutions for the load power transfer and energy harvesting cases. The results indicate that entropy generation minimization is akin to the maximum power transfer theorem. For the power harvesting case, closed-loop stability is guaranteed and practical controllers may be designed. The approach is compared against direct minimization of losses, both theoretically and with Monte Carlo simulations. Full article

In response to the performance requirements of ship conductive rings in the coupled environment of high salt spray, high humidity, and mechanical wear in the ocean, a Cu-TiC composite coating was prepared on the surface of 7075 aluminum alloy by using the high-speed laser cladding (HLC) technology. The influence laws of the scanning speed (86.4–149.7 mm/s) on the microstructure, tribological properties, and corrosion resistance of the coating were explored. The results show that the scanning speed significantly changes the phase composition and grain morphology of the coating by regulating the thermodynamic behavior of the molten pool. At a low scanning speed (86.4 mm/s), the CuAl₂ phase is dominant, and the grains are mainly columnar crystals. As the scanning speed increases to 149.7 mm/s, the accelerated cooling rate promotes an increase in the proportion of Cu₂Al₃ phase, refines the grains to a coexisting structure of equiaxed crystals and cellular crystals, and improves the uniformity of TiC particle distribution. Tribological property analysis shows that the high scanning speed (149.7 mm/s) coating has a 17.9% lower wear rate than the substrate due to grain refinement and TiC interface strengthening. The wear mechanism is mainly abrasive wear and adhesive wear, accompanied by slight oxidative wear. Electrochemical tests show that the corrosion current density of the high-speed cladding coating is as low as 7.36 × 10⁻⁷ A·cm⁻², and the polarization resistance reaches 23,813 Ω·cm². The improvement in corrosion resistance is attributed to the formation of a dense passivation film and the blocking of the Cl diffusion path. The coating with a scanning speed of 149.7 mm/s exhibits optimal wear-resistant and corrosion-resistant synergistic performance and is suitable for the surface strengthening of conductive rings in extreme marine environments. This research provides theoretical support for the process performance regulation and engineering application of copper-based composite coatings. Full article

Quantum field theory (QFT) and general relativity (GR) are pillars of modern physics, each supported by extensive experimental evidence. QFT operates within Lorentzian spacetime, while GR ensures local Lorentzian geometry. Despite their successes, these frameworks diverge significantly in their estimations of vacuum energy density, leading to the cosmological constant problem—a discrepancy where QFT estimates exceed observed values by 123 orders of magnitude. This paper addresses this inconsistency by tracing the cooling evolution of the universe’s gauge symmetries—from $SU\left(3\right)\times SU\left(2\right)\times U\left(1\right)$ at high temperatures to $SU\left(3\right)$ alone near absolute zero—motivated by the experimental Meissner effect. This symmetry reduction posits that $SU\left(3\right)$ forms the fundamental “atoms” of vacuum energy. Our analysis demonstrates that the calculated number of $SU\left(3\right)$ vacuum atoms reconciles QFT’s predictions with empirical observations, effectively resolving the cosmological constant problem. The third law of thermodynamics, by preventing the attainment of absolute zero, ensures the stability of $SU\left(3\right)$ vacuum atoms, providing a thermodynamic foundation for quark confinement. This stability guarantees a strictly positive mass gap defined by the vacuum energy density and implies a Lorentzian quantum structure of spacetime. Moreover, it offers insights into the origins of both gravity/gauge duality and gravity/superconductor duality. Full article