Advanced finite-element analyses are increasingly being used in geotechnical design, and central to these analyses are reliable and accurate constitutive models to represent soil behaviour. These models need to address response across a wide range of conditions, including for instance cyclic loading for offshore applications. Existing advanced constitutive models for sand have limited capability for modelling cyclic loading, are often complex and rarely respect the laws of thermodynamics. HySand_base, a new constitutive model for sand under cyclic loading, is presented. Its concise, rigorous and simple formulation within the hyperplasticity framework is given. Each element of the formulation is explained through the progressive construction of the model, and the improvements brought by each additional feature are illustrated for drained monotonic, undrained monotonic and undrained cyclic tests. HySand_base uses 14 material parameters. It is a density- and pressure-dependent multi-surface plasticity model, rooted in critical state theory, with yield surfaces based on the fusion of Matsuoka–Nakai type surfaces with consolidation surfaces. Non-associated plasticity is adopted, with volumetric plastic strains arising from two mechanisms: anisotropic dilation and consolidation.

Insights and hindsights into the molecular mechanism of ATP hydrolysis by muscle myosin, kinesin/unconventional myosins, and axonemal dynein motors.

The challenge of understanding quantum measurement persists as a fundamental issue in modern physics. Particularly, the abrupt and energy-nonconserving collapse of the wave function appears to contradict classical thermodynamic laws. The contradiction can be resolved by considering measurement itself to be an entropy-increasing process, driven by the second law of thermodynamics. One such resolution explains the apparently irreversible emergence of objective outcomes in an isolated, unitarily evolving quantum system via the theory of closed-system equilibration. Working within this framework, we construct the set of “” that best encode the measurement statistics of a system in an objective manner and establish a measurement error bound to quantify the probability an observer will obtain an incorrect measurement outcome. Using this error bound, we show that the objectifying observables readily equilibrate on average under the set of Hamiltonians which preserve the outcome statistics on the measured system. Using a random matrix model for this set, we numerically determine the measurement error bound, finding that the error only approaches zero with increasing environment size when the environment is coarse grained into so-called observer systems. This indicates the necessity of coarse graining an environment for the emergence of objective, classical measurement outcomes.

Understanding the melting behavior at the nanoscale regime serves a fundamental role in both the scientific community and industrial applications. In particular, the melting of nanoparticles (NPs) exhibits behaviors that differ qualitatively from bulk materials due to pronounced size-dependent properties and surface/volume ratio effects, but a unified theoretical understanding remains elusive. Here, by developing a machine-learning interatomic potential applicable across diverse local atomic environments and wide temperature ranges, we systematically investigate the melting thermodynamics of Au NPs spanning from small clusters (102 atoms) to large NPs (105 atoms) through a series of nanosecond-long molecular dynamics simulations. A complete solid-liquid phase diagram of NPs across 1-14nm diameters is presented, clearly distinguishing the unique surface premelting behavior and complete melting. The size-dependent melting curve follows the Gibbs-Thomson relationship. More importantly, we demonstrate that the melting entropy changes in nanoparticle systems substantially deviate from the empirical Richard's rule and its generalized form valid for bulk elemental systems. Moreover, we found that all the components of melting entropy follow the same scaling law, based on which we derived a thermodynamic correlation between the NP system and its bulk values. These results bridge the thermodynamic description from the single-atom limit to bulk materials, providing a unique insight for understanding and predicting nanoscale melting thermodynamics.

Abstract Open quantum systems play a central role in current nanoscale technologies, such as molecular electronics, quantum heat engines, quantum computation and information processing. A major theoretical challenge is to construct dynamical models that are simultaneously consistent with classical thermodynamics and with the requirement of complete positivity of quantum evolution. In this work we develop a framework that addresses this issue by systematically extending classical stochastic dynamics to the quantum domain. We begin by formulating a generalized Langevin equation in which both friction and noise act symmetrically on the two Hamiltonian equations. From this, we derive a generalized Klein–Kramers equation expressed in terms of Poisson brackets, and we show that it admits the Boltzmann distribution as its stationary solution while fulfilling the first and second laws of thermodynamics along individual trajectories. Applying canonical quantization to this classical framework yields two distinct quantum master equations, depending on whether the friction operators are taken to be Hermitian or non-Hermitian. By analyzing the dynamics of a harmonic oscillator, we determine the conditions under which these equations reduce to a Lindblad-type generator. Our results demonstrate that complete positivity is ensured only when friction and noise are included in both Hamiltonian equations, fully justifying the classical construction. Moreover, we find that the friction coefficients must adhere to the same positivity condition in both the Hermitian and non-Hermitian formulations, revealing a form of universality that transcends the specific operator representation. The formalism developed here presents a thermodynamically consistent and completely positive quantum extension of classical stochastic mechanics. It offers a versatile tool for deriving quantum versions of thermodynamic laws and is directly applicable to a broad class of non-equilibrium nanoscale systems of current theoretical and technological interest.

This short communication proposes criteria to be considered suitable candidates from among the various versions of the fourth law of thermodynamics.

Einstein-bumblebee gravity is one of the simplest vector-tensor theories that realizes spontaneous Lorentz symmetry breaking. In this work, we first construct an exact dyonic Reissner-Nordström-like black hole solution in four dimensions, carrying both electric and magnetic charges and admitting general topological horizons. We then study its thermodynamic properties, and employ the Wald formalism to compute the conserved mass and entropy, thereby establishing the first law of black hole thermodynamics. Furthermore, we generalize these results to Taub-Newman-Unti-Tamburino case and higher dimensions case.

In a dissipative system such as star or a galaxy, the emitted photons are decoupled from matter particles and may therefore be considered as part of a closed system to which the second law of thermodynamics applies. In the present work, I defined a global entropy using a statistical approach that accounts for the contributions of both matter particles and photons. The statistical contribution of radiation is described as a photon gas in the definition of this global entropy. The increase in global entropy can foster structure formation –rather than disorder– because structures such as stars and galaxies are efficient in dissipating energy in the form of photons, and thus in producing entropy. I show that stars generate a nearly equal amount of specific entropy and, therefore, a comparable number of photons per unit mass over their lifetime on the main sequence of the Hertzsprung–Russell (HR) diagram. This suggests that the main sequence of the HR diagram constitutes a locus of convergence toward a universal specific entropy production by stars. I then examined the implications of this approach for the star-formation main sequence in galaxies and found a similar result. The emergence of organized structures in cosmic history reflects the second law, as organized matter is efficient in generating entropy through the slicing of energy into lower frequency photons. This is also reflected in the dominant contribution of low-frequency photons to the extragalactic background light. Finally, in this paper I briefly discuss how this perspective may provide insight into the possibility of the existence of life elsewhere in the Universe.

Formulation of the Principle of Energy Quality: Toward a Fourth Law of Thermodynamics

The increasing use of deep coal mine backfilling operations under high geothermal conditions has drawn attention, The growing application of deep coal mine backfilling under elevated geothermal conditions has attracted increasing attention; however, the role of curing temperature in governing the mechanical response and energy evolution of coal-based solid waste backfill has not yet been fully clarified. In this study, coal gangue, fly ash, and desulfurization gypsum were selected as representative coal-based solid waste constituents to systematically examine the mechanical behavior and energy evolution of cemented backfill subjected to different curing temperatures (20, 27.5, 35, 42.5, and 50 °C) and curing durations (3, 7, 14, and 28 d). Material characteristics were characterized using X-ray diffraction (XRD), scanning electron microscopy (SEM), and particle size distribution analysis. Displacement-controlled uniaxial compression tests were conducted to obtain stress–strain responses, while elastic strain energy and dissipated energy were quantified and analyzed on the basis of the first law of thermodynamics. The findings highlight that curing temperature has a marked age-dependent effect on the mechanical behavior of the backfill. At early ages (3, 7, and 14 days), increasing the curing temperature enhances the elastic modulus, peak stress, and peak strain. At 28 days, both strength and deformation capacity reach their maximum values at 42.5 °C, whereas increasing the temperature to 50 °C causes post-peak softening and a reduction in load-bearing capacity. Energy analysis reveals that, at 28 days, both elastic strain energy and total energy at the peak stress first rise and then decline as curing temperature increases, reaching maximum values of 35.92 kJ/m³ and 56.45 kJ/m³, respectively, at 42.5 °C. The energy evolution process can be categorized into four distinct stages: pore compaction, linear elastic deformation, yielding damage, and post-peak failure. Higher curing temperatures significantly increase the proportion of energy dissipated in the compaction stage (from 37.5% to 59.3%) while reducing the energy dissipated in the elastic stage, which accelerates the damage process under high-temperature curing.

A bstract We construct, for the first time, new static non-extremal five-dimensional black hole solutions (without or with squashed horizons) endowing with four different electric charge parameters in the D = 5, $$ \mathcal{N} $$ N = 2 supergravity coupled to three vector multiplets with a specific pre-potential $$ \mathcal{V} $$ V = STU – W 2 U ≡ 1. When the fourth charge parameter disappears, the solution simplify reduces to the three-charge static black hole solution previously presented in ref. [1], which belongs to the solution to the D = 5, $$ \mathcal{N} $$ N = 2 supergravity coupled to two vector multiplets (also notably known as the STU model). We parameterize the model in such a simple fashion that not only can one easily recover the static three-charge solution but also it is very convenient to study their thermodynamical properties of the obtained black hole solutions in the case without a squashing horizon. We then show that the thermodynamical quantities perfectly obey both the differential first law and integral Smarr formula of thermodynamics. Finally, we also extend to present its generalizations with squashed horizons or including a nonzero cosmological constant.

We construct the first self-consistent framework for holographic thermodynamics in finite-cutoff holography, thereby capturing gravitational thermodynamics beyond the anti-de Sitter (AdS) boundary. We formulate two distinct first laws of thermodynamics: for the gravitational bulk, a Schwarzschild-AdS black hole with a finite Dirichlet cutoff, and for its dual T 2 deformed conformal field theory (CFT) on the boundary. The central innovation is promoting the deformation parameter to a thermodynamic variable on the boundary, which maps precisely to the cutoff radius in the bulk. We demonstrate exact duality between these two thermodynamic laws, establishing a complete holographic dictionary. This framework reveals that the T 2 deformation never lowers the confinement-deconfinement phase transition temperature below that of the original undeformed CFT, which acts as a global minimum. These results offer insights into gravitational thermodynamics with boundary constraints and quantum gravity in finite spacetime regions.

As the core pressure-regulating component of the Electronic Controlled Pneumatic Braking System (ECPBS) for commercial vehicles, the Automatic Pressure Regulating Valve (APRV) directly determines the accuracy and responsiveness of brake pressure adjustment, which is crucial for ensuring braking safety, stability, and ride comfort—especially in the context of autonomous driving. The pressure change rate is a key indicator reflecting braking smoothness and dynamic response performance, and its accurate calculation is the foundation for optimizing braking control strategies. To address the complexity and computational inefficiency in calculating the pressure change rate of multi-component, nonlinear APRV systems, this study proposes an equivalent calculation method based on throttle orifice flow characteristics. By equating the openings and chambers of an APRV to throttling orifices (fixed and variable) and variable-volume cavities, we simplified the complex pneumatic system while preserving its core dynamic characteristics. Theoretical derivation was conducted by integrating the first law of thermodynamics, ideal gas law, and flow equations for fixed/variable throttle orifices to establish a pressure change rate calculation model. The validity of the proposed method was verified through theoretical analysis, numerical simulation, and experimental testing. Compared with existing models, the proposed method achieved a balance between calculation accuracy and efficiency, with the simulation error within 2% (pressure) and 10% (pressure change rate), and it significantly improved computational efficiency compared to conventional models. This research provides a concise and accurate theoretical tool for the rapid prediction and precise control of pressure change rate in ECPBS, which is of great significance for optimizing autonomous driving braking planning, enhancing braking ride comfort by reducing vehicle jerk, and promoting the development of active safety technologies. The proposed equivalent modeling approach also offers a reference for the performance analysis of similar complex pneumatic components or systems.

Abstract In this article, in terms of the first and second laws of thermodynamics, as well as the principle of maximum energy dissipation rate, a continuum elastic-plastic theory for porous materials is proposed. Unlike the Prandtl-Reuss equation, the influence of plastic volumetric strain is fully taken into account. An incremental elastic-plastic constitutive law is derived, and a series of yield criteria is proposed. Its implementation is demonstrated with a simple example. This study offers a new perspective for modeling the elastic-plastic deformation of porous materials.

Increasing the efficiency and durability of the piston compressors, pumps, internal combustion engines, etc. directly depends on the correct calculations and designing of these elements. Using ANSYS software, simulation and stress analysis are performed on the basis of the 405GP15/70 and ARIEL heavy-duty balanced opposed piston compressors used in the Caspian Sea - Black Sea Region, providing numerical validation of thermal and structural behavior under operational conditions. Investigation of complex problems with respect to stresses, and thermodynamics phenomena in the piston machines, and oil and gas pipelines gives the opportunity to solve the problems of increasing the durability of these machines and pipelines. Increasing the reliability and durability of piston machines therefore meets the current industrial demand for minimizing environmental impacts during the exploitation and transportation of oil and gas resources. The novelty is characterized by new theoretical methods for the determination of forces of gas pressure in cylinders of reciprocating machines taking into account the wear processes and the clearances in kinematic couples of crank-piston mechanisms. The reliability of the received scientific results is provided with the correctness of the statement of tasks and decisions on the basis of laws of physics, mechanics and thermodynamics. The results of the investigation are generalized for any piston machines used in the oil and gas industry. The results of the investigation can be useful for the design and exploitation of transregional pipelines and environmental problems.

In this paper, we obtain possible cosmologies without big bang singularity. We first get effective modifications of Friedmann equations by using a texture of the first law of thermodynamics with our proposed generalization of the Bekenstein–Hawking entropy. We get modified Friedmann equations leading to a universe without big bang singularity and with maximum allowed values for the Hubble flow, i.e. [Formula: see text], and for the energy density, i.e. [Formula: see text]. A general study of solutions of the aforementioned equations shows that an emergent universe filled with non-phantom matter arises starting with [Formula: see text] and with an exponential form for the scale factor [Formula: see text] corrected by a decreasing exponential together with regular expressions for [Formula: see text] everywhere. A further feature of these models is that the time derivative of [Formula: see text] ([Formula: see text]) when [Formula: see text] is reached is diverging, also by considering further quantum corrections. Finally, we show that a universe with finite [Formula: see text] can be easily obtained, for example, with a smooth transition from a phantom universe to a non-phantom one. In this way, we obtain a regular universe with a quasi-de Sitter phase emerging naturally after Planckian times [Formula: see text] without fine tuning.

Amid the global energy structure's profound transformation and full implementation of the dual carbon strategy, optimal planning of integrated energy systems (IESs) is a cutting-edge energy topic. Most relevant studies rely on the first law of thermodynamics, focusing on energy conservation, while integration of energy quality, thermodynamics, and economics remains to be improved. This study takes the planning phase of IESs as the entry point and proposes an analytical method with exergy theory as the core and exergoeconomics as the tool. It proposes a closed-loop full-process planning framework of "theoretical modeling-scheme construction-economic analysis-scheme improvement" to develop a mature, replicable IES planning model, providing theoretical and technical support for the energy system's low-carbon transformation. Standard case simulations validate the efficacy of the closed-loop planning framework in enhancing system exergy efficiency and optimizing economic costs, providing engineering decision support and insights for multidisciplinary paradigm advancement.

Mitochondria are central hubs of cellular bioenergetics, converting chemical free energy into ATP while inevitably releasing heat during respiration. Fluorescence-based thermometry has been interpreted to show intracellular "hot spots" more than 10 °C above the bulk physiological temperature, implying that mitochondria might operate far outside conventional thermal bounds. Such claims, however, appear inconsistent with basic biophysics: the small size of mitochondria, their aqueous and highly conductive environment, and their limited power output all argue against large steady-state temperature gradients. This discrepancy has prompted renewed scrutiny of both the physical limits of intracellular heat transfer and the biological interpretation of nanoscale thermal measurements. A key open question is whether nonequilibrium biochemical processes, such as respiration-driven proton pumping, could act as nanoscale heat pumps that maintain higher local temperatures than allowed by passive diffusion alone. Here, we develop a model-independent thermodynamic analysis based solely on the Second Law of Thermodynamics to bound the maximal temperature difference that any biochemically driven mechanism can sustain across the inner mitochondrial membrane and show that even under idealized conditions the achievable temperature rise is restricted to a small fraction of a degree, effectively closing this loophole.

Abstract Modern society is under the illusion that calculation and measurement amounts to control. Heidegger’s critique of the enchantment of modernity shows how the machinations of power are inhibiting the course of evolving change. People cannot reflect on the real failures of the many iterations of the polycrisis and learn from them. This failure to notice failure is at the core of the metacrisis. Modern society is under the illusion that progress as continuous exponential growth can proceed with its onward trajectory without having a profound impact on resources, pollution, socio-cultural and ecological well-being. Education remains entrapped within the enchantment of modernity, and continues to prioritise the calculation and control easily imposed on STEM subjects, and the development of rationality as “progress” over and above a more wholistic approach to education. But the pace of planetary cycles and laws of thermodynamics bind humanity as much as they do other species. Understanding how finance supercharges the economic growth cycle will help us to re-evaluate and learn from the failures of the metacrisis, and transition to a calmer, slow economic system and more egalitarian future.

This paper builds upon a 2024 IJMEE paper, which formally established the logical equivalence of the first and second laws of thermodynamics. Logical equivalence means that both laws are either true or false together; however, this does not imply that the laws are identical or necessarily derivable from one another. As stated in the 2024 paper, “… if we can know that the first and second laws are equivalent, then we should know.” Accordingly, the present work investigates how this equivalence informs our understanding of heat engine cycles. Through a truth table analysis and application to real and hypothetical heat engine cycles , this paper shows that a violation of one law necessitates the violation of the other, even if numerical calculations appear to suggest otherwise. Understanding this relationship not only clarifies the interconnectedness of the two laws but also provides students and educators with a valuable conceptual framework for analyzing thermodynamic systems. This insight enriches problem-solving strategies and reinforces the critical role of equilibrium and energy conservation in determining the feasibility of thermodynamic processes.