Law Of Thermodynamics Research Articles

Gravitational collapse to extremal black holes and the third law of black hole thermodynamics

We construct examples of black hole formation from regular, one-ended asymptotically flat Cauchy data for the Einstein–Maxwell-charged scalar field system in spherical symmetry which are exactly isometric to extremal Reissner–Nordström after a finite advanced time along the event horizon. Moreover, in each of these examples the apparent horizon of the black hole coincides with that of a Schwarzschild solution at earlier advanced times. In particular, our result can be viewed as a definitive disproof of the “third law of black hole thermodynamics.” The main step in the construction is a novel C^{k} characteristic gluing procedure, which interpolates between a light cone in Minkowski space and a Reissner–Nordström event horizon with specified charge to mass ratio \frac{e}{M} . Our setup is inspired by the recent work of Aretakis–Czimek–Rodnianski on perturbative characteristic gluing for the Einstein vacuum equations. However, our construction is fundamentally nonperturbative and is based on a finite collection of scalar field pulses which are modulated by the Borsuk–Ulam theorem.

Thermodynamic Approach to Modeling Complexity of Regional Hewett-Hubbert Resource Bubbles and Large Dynasties

This paper examines how the phenomena of emergence and complexity can be applied to the analysis of physical Hewett-Hubbert resource bubbles and historical dynasties. Concepts and definitions of energy, the laws of thermodynamics, efficiency, power and other useful terminology are introduced. Relevant proposed extensions of the Second Law of Thermodynamics are discussed. Several definitions of complexity are discussed and critiqued, including the energy rate density approach. Approaches between energy rate density and entropy approaches are compared. The divergence between energy rate density and complexity artifacts is explored. Principles of extended thermodynamics are then applied to the emergence of medium-term dissipative structures, such as the rise and fall of physical resource bubbles and historical dynasties. Changes in complexity are discussed when resource bubbles and historical dynasties progress through their processes of emergence. Patterns in complexity change are identified and a characteristic complexity profile for resource bubbles and historical dynasties is articulated.

The information conservation in Hawking radiation by laws of thermodynamics

By solving the field equation in curved spacetime, we obtained the relative emissivity of the Kerr–Newman black hole. The results show that the relative emissivity satisfies the Boltzmann distribution law. With the first law of thermodynamics, we found that the emissivity is related to the entropy change of black holes which helps us solve the information loss in the Hawking radiation. Through calculating the information entropy of black holes, it is shown that the information conservation is satisfied in the Hawking radiation. Furthermore, we also studied the contribution of space-time background to Hawking radiation.

Phantom hairy black holes and wormholes in Einstein-bumblebee gravity

In this paper we study Einstein-bumblebee gravity theory minimally coupled with external matter – a phantom/non-phantom (conventional) scalar field, and derive a series of hairy solutions – bumblebee-phantom (BP) and BP-dS/AdS black hole solutions, regular Ellis-bumblebee-phantom (EBP) and BP-AdS wormholes, etc. We first find that the Lorentz violation (LV) effect can change the so-called black hole no-hair theorem and these scalar fields can give a hair to a black hole. If LV coupling constant ℓ>-1-1$$\\end{document}]]>, the phantom field is admissible and the conventional scalar field is forbidden; if ℓ<-1, the phantom field is forbidden and the conventional scalar field is admissible. By defining the Killing potential ωab, we study the Smarr formula and the first law for the BP black hole, find that the appearance of LV can improve the structure of these phantom hairy black holes – the conventional Smarr formula and the first law of black hole thermodynamics still hold; but for no LV case, i.e., the regular phantom black hole reported in (Phys Rev Lett 96:251101), the first law cannot be constructed at all. We also show there still exists a stable circular orbit around the BP black hole. When the bumblebee potential is linear, we find that the phantom potential and the Lagrange-multiplier λ behave as a cosmological constant Λ.

Environmental Economics and Ecological Economics: Historical Evolution and the Current Status

The nomenclatures ‘environmental economics’ and ‘ecological economics’ are frequently utilised interchangeably in academic and policy spheres. While purportedly complementary in certain aspects, these disciplines diverge significantly in various fundamental principles. Environmental economics boasts a lengthy lineage, with its conceptual foundations traceable to pre-classical economic thought. On the other hand, ecological economics emerged more recently, particularly in the post-1980s, articulating ecological and energy-related concepts beyond the purview of neoclassical-based environmental economics. Although the distinctions between these two fields of inquiry in environment–human interactions have been well established in global academia, such delineations remain inadequately articulated within the Indian context. Consequently, the development of environmental curricula in economics departments predominantly revolves around environmental economics, often lacking critical inputs from ecological economics. In some instances, curricula incorporate an amalgamation of theories, concepts, principles and methodologies from both fields, leading to conceptual ambiguity. Furthermore, the lack of awareness among educators and students regarding these distinctions results in the treatment of both fields as synonymous, thereby limiting exposure to critical aspects of the alternative discipline. This article presents a systematic review of the historical evolution of neoclassical-based environmental economics and argues that ecological economics emerged as a ‘reaction’ to reorient the former with relevant inputs from domains such as political ecology and the laws of thermodynamics. The analysis aims to clarify the demarcations between these two significant branches of economic thought in the context of environmental studies.

Quantifying Thermal Transport in 3D Printed Fractal Structures

Abstract Heat transport through 3D printed fractal media is investigated by comparing a fractal diffusion model to infrared measurements using Bayesian uncertainty quantification. The Delayed Rejection Adaptive Metropolis (DRAM) algorithm, based on the Markov Chain Monte Carlo (MCMC) sampling technique, is used to infer parameter uncertainty, quantify parameter correlation, and compute error propagation of the temperature distributions. The results demonstrate that fractal operators improve modeling thermal transport through complex fractal structures and help understand fractal structure-property relationships. For example, correlations among fractal spatial and temporal scaling parameters, diffusion coefficients, and fractal dimensions are quantified. We find a scaling relationship between the diffusion coefficient D and the temporal fractal time derivative order α that scales nominally as D α eα based on constraints from the second law of thermodynamics. The results have implications for building a stronger understanding of heat transport in complex materials beyond random media and models based on Gaussian probability homogenization.

Tantum gravity

We argue there is an interesting triple-scaling limit of quantum gravity, namely when Planck’s constant scales to infinity while Newton’s constant and the speed of light tend to zero, keeping fixed the gravitational coupling GNc−4 and the combination ℏc. We refer to this limiting theory as “tantum gravity” and describe in this Letter some of its main properties and prospects for physics. Most notably, the laws of black hole thermodynamics survive this limit, which means that puzzles related to black holes and their evaporation could be addressed more easily in tantum gravity than in fully fledged quantum gravity. Published by the American Physical Society 2025

Thermodynamics of Surfactant-Enriched Binary-Fluid Systems.

Surface-active agents (surfactants) release potential energy as they migrate from one of two adjacent fluids onto their fluid-fluid interface, a process that profoundly impacts the system's energy and entropy householding. The continuum thermodynamics underlying such a surfactant-enriched binary-fluid system has not yet been explored comprehensively. In this article, we present a mathematical description of such a system, in terms of balance laws, equations of state, and permissible constitutive relations and interface conditions, that satisfies the first and second law of thermodynamics. The interface conditions and permissible constitutive relations are revealed through a Coleman-Noll analysis. We characterize the system's equilibrium by defining equilibrium equivalences and study an example system. With our work, we aim to provide a systematically derived framework that combines and links various elements of existing literature, and that can serve as a thermodynamically consistent foundation for the (numerical) modeling of full surfactant-enriched binary-fluid systems.

Holographic thermodynamic relation for dissipative and non-dissipative universes in a flat FLRW cosmology

Horizon thermodynamics and cosmological equations in standard cosmology provide a holographic-like connection between thermodynamic quantities on a cosmological horizon and in the bulk. It is expected that this connection can be modified as a holographic-like thermodynamic relation for dissipative and non-dissipative universes whose Hubble volume V varies with time t. To clarify such a modified thermodynamic relation, the present study applies a general formulation for cosmological equations in a flat Friedmann–Lemaître–Robertson–Walker (FLRW) universe to the first law of thermodynamics, using the Bekenstein–Hawking entropy SBH and a dynamical Kodama–Hayward temperature TKH. For the general formulation, both an effective pressure pe of cosmological fluids for dissipative universes (e.g., bulk viscous cosmology) and an extra driving term fΛ(t) for non-dissipative universes (e.g., time-varying Λ(t) cosmology) are phenomenologically assumed. A modified thermodynamic relation is derived by applying the general formulation to the first law, which includes both pe and an additional time-derivative term f˙Λ(t), related to a non-zero term of the general continuity equation. When fΛ(t) is constant, the modified thermodynamic relation is equivalent to the formulation of the first law in standard cosmology. One side of this modified relation describes thermodynamic quantities in the bulk and can be divided into two time-derivative terms, namely ρ˙ and V˙ terms, where ρ is the mass density of cosmological fluids. Using the Gibbons–Hawking temperature TGH, the other side of this relation, TKHS˙BH, can be formulated as the sum of TGHS˙BH and [(TKH/TGH)-1]TGHS˙BH, which are equivalent to the ρ˙ and V˙ terms, respectively, with the magnitude of the V˙ term being proportional to the square of the ρ˙ term. In addition, the modified thermodynamic relation for constant fΛ(t) is examined by applying the equipartition law of energy on the horizon. This modified thermodynamic relation reduces to a kind of extended holographic-like connection when a constant TKH universe (whose Hubble volume varies with time) is considered. The evolution of thermodynamic quantities is also discussed, using a constant TKH model, extending a previous analysis (Komatsu in Phys Rev D 108:083515, 2023).

Density Functional Study on the Condensation and Evaporation Heats of the Nanoconfined Fluids.

Within the framework of classical density functional theory, the isosteric heat and condensation/evaporation heat of the confined methane are studied. First, the theoretical expression for condensation/evaporation heat is derived on the basis of the first law of thermodynamics. The method for computation is also proposed. With the proposed method, the dependences of the condensation/evaporation heat on temperature, pore width, and surface strength are studied and analyzed in detail. First of all, it is found that the condensation/evaporation heat of the confined fluid decreases monotonically with the temperature. Moreover, it is also found that at the same temperature the condensation heat is usually larger than the corresponding evaporation heat, which confirms the irreversibility of the condensation and evaporation from an exothermic point of view. Furthermore, our results reveal that the condensation/evaporation heat of confined fluid in pores decreases with the width of the pore. With the further increase in the pore width, the condensation/evaporation heat tends gradually to that of the corresponding bulk fluids. In addition, an interesting result is found that the condensation/evaporation heat is insensitive to variation in surface strength.

Emergence of a Second Law of Thermodynamics in Isolated Quantum Systems

The second law of thermodynamics states that the entropy of an isolated system can only increase over time. This appears to conflict with the reversible evolution of isolated quantum systems under the Schrödinger equation, which preserves the von Neumann entropy. Nonetheless, one finds that with respect to many observables, expectation values approach a fixed value—their equilibrium value. This ultimately raises the question: ? For classical systems, one introduces the assumption of a low-entropy initial state along with the concept of ignorance about the microscopic details of the physical system, leading to a statistical interpretation of the second law. By considering the observables through which we examine quantum systems, both these assumptions can be incorporated, building upon recent studies of the of observables. While the statistical behavior of observable expectation values is well established, a quantitative connection to entropy increase has been lacking so far. In deriving novel bounds for the equilibration of observables, and considering the entropy of the system relative to observables, we recover a variant of the second law: the entropy with respect to a given observable tends toward its equilibrium value in the course of the system’s unitary evolution. These results also support recent findings that question the necessity of nonintegrability for equilibration in quantum systems. We further illustrate our bounds using numerical results from the paradigmatic example of a quantum Ising model on a chain of spins. There, we observe entropy increasing up to equilibrium values, as well as fluctuations, which expose the underlying reversible evolution in accordance with the derived bounds. Published by the American Physical Society 2025

Comprehensible dynamics of quanta: from the quantum of action to the 2nd law of thermodynamics

The 2nd law of thermodynamics is derived from the principle of least action, positing that the quantum of action is the indivisible and indestructible basic building block of everything. On their least-time paths to balance, the quanta move from the system to its surroundings, or vice versa, so that the kinetic, potential, and dissipated energy tally. When re-expressed in logarithmic terms, this current toward more probable states with decreasing free energy equates to the principle of increasing entropy, the 2nd law of thermodynamics, including path-independent dynamic and path dependent geometric phase shifts. Despite being exact, the equation of evolution to entropy maximum, equivalent to free energy minimum, cannot be solved because evolution, consuming its own driving forces, becomes path dependent. Thus, the future remains open within free energy bounds. As discussed, the entropy derived from the statistical physics of open quantum systems sums states distinguishable in energy; whereas, Boltzmann’s entropy enumerates microstates indistinguishable in energy. Consequently, the statistical physics of open systems differs from that of closed systems: The irreversible evolution in the state space toward thermodynamic balance contrasts with the steady-state revolution in phase space between conceivable configurations. This concrete comprehension explains, among other things, that increasing disorder is not a law of nature itself but a consequence of the law to attain balance with incoherent surroundings in the least time.

Thermodynamic aspects of higher-dimensional black holes in Einstein–Gauss–Bonnet gravity through exponential entropy

Abstract We assume exponential corrections to the entropy of $5D$ charged AdS&amp;#xD;black hole solutions, which are derived within the framework of&amp;#xD;Einstein Gauss-Bonnet gravity and nonlinear electrodynamics.&amp;#xD;Additionally, we consider two distinct versions of $5D$ charged AdS&amp;#xD;black holes by setting the parameters $q\rightarrow0$ and&amp;#xD;$k\rightarrow0$ (where $q$ represents charge, $k$ is the non-linear&amp;#xD;parameter). We investigate these black holes in the extended phase&amp;#xD;space, where the cosmological constant is interpreted as pressure,&amp;#xD;and demonstrate the first law of black hole thermodynamics. The&amp;#xD;focus extends to understanding the thermal stability or instability,&amp;#xD;as well as identifying first and second-order phase transitions.&amp;#xD;This exploration is carried out through the analysis of various&amp;#xD;thermodynamic quantities, including heat capacity at constant&amp;#xD;pressure, Gibbs free energy, Helmholtz free energy, and the trace of&amp;#xD;the Hessian matrix. In order to visualize phase transitions,&amp;#xD;identify critical points, analyzing stability and provide&amp;#xD;comprehensive analysis, we have made the contour plot of the&amp;#xD;mentioned thermodynamic quantities and observed that our results are&amp;#xD;very much consistent. These investigations are conducted within the&amp;#xD;context of exponentially corrected entropies, providing valuable&amp;#xD;insights into the intricate thermodynamic behavior of these $5D$&amp;#xD;charged AdS black holes under different parameter limits.

Challenging the Green Machine: Rejoinder to Schwartzman

ABSTRACT We respond to David Schwartzman’s critique of our paper. We argue that his “solar communism,” his approach to the question of energy return on energy investment (EROI), and his critique of Georgescu-Roegen’s fourth law of thermodynamics situate him as a left ecomodernist, albeit with sympathy for degrowth. Schwartzman’s take on these issues illustrates how the ontological separation of human ingenuity and global social metabolism obscures the question of for whom a high-energy modern society is possible. This is further exacerbated by his commitment to the notion of perfect recycling, which has been proven practically impossible in inorganic systems.

Improving the teaching of entropy and the second law of thermodynamics: a systematic review with meta-analysis

Entropy and the second law of thermodynamics have long been identified as difficult concepts to teach in the physical chemistry curriculum. Their highly abstract nature, mathematical complexity and emergent nature underscore the necessity to better link classical thermodynamics and statistical thermodynamics. The objectives of this systematic review are thus to scope the solutions suggested by the literature to improve entropy teaching. ERIC and SCOPUS databases were searched for articles aiming primarily at this objective, generating N = 315 results. N = 91 articles were selected, among which N = 9 reported quantitative experimental data and underwent a meta-analysis, following PRISMA guidelines. Risk of bias was assessed by the standards criteria of What Works Clearinghouse. Results from the qualitative selection show diverse solutions to solve the entropy teaching hurdles, such as connection to everyday life, visualization, mathematics management by demonstrations, games and simulations, criticism and replacement of the disorder metaphor and curriculum assessment. The synthetic meta-analysis results show high but uncertain effect sizes. Implications for teachers and researchers are discussed.

Waste Heat and Habitability: Constraints from Technological Energy Consumption.

Waste heat production represents an inevitable consequence of energy conversion as per the laws of thermodynamics. Based on this fact, by using simple theoretical models, we analyze constraints on the habitability of Earth-like terrestrial planets hosting putative technological species and technospheres characterized by persistent exponential growth of energy consumption and waste heat generation. In particular, we quantify the deleterious effects of rising surface temperature on biospheric processes and the eventual loss of liquid water. Irrespective of whether these sources of energy are ultimately stellar or planetary (e.g., nuclear, fossil fuels) in nature, we demonstrate that the loss of habitable conditions on such terrestrial planets may be expected to occur on timescales of ≲1000 years, as measured from the start of the exponential phase, provided that the annual growth rate of energy consumption is of order 1%. We conclude with a discussion of the types of evolutionary trajectories that might be feasible for industrialized technological species, and we sketch the ensuing implications for technosignature searches.

Brownian motion in the Hilbert space of quantum states along with the Ricci flow and stochastically emergent Einstein–Hilbert action: Formulating a well-defined Feynman’s path-integral measure for quantum fields in the presence of gravity

In this paper, we aim to interpret the background gravitational effects appearing in quantum field theory on curved space-time by studying the Brownian motion of quantum states along with the Hamilton–Perelman Ricci flow. It has been shown that the Wiener measure automatically contains the Einstein–Hilbert action and the path-integral formulation of the scalar quantum field theory on curved space-time at the first order of local approximations. This provides a well-defined formulation of the path-integral measure for quantum field theory in the presence of gravity. However, we establish that the emergence of Einstein–Hilbert action is independent of the matter field interactions and is a merely entropic/geometric effect stemming from the nature of the Ricci flow of the universe geometry. We also extract an explicit formula for the cosmological constant in terms of the Ricci flow and Hamilton’s theorem for 3-manifolds. Then, we discuss the cosmological features of the FLRW solution in [Formula: see text]CDM Model via the derived equations of the Ricci flow. We also argue the correlation between our formulations and the entropic aspects of gravity. Finally, we provide some theoretical evidence that proves the second law of thermodynamics is the basic source of gravity and probably a more fundamental concept.

KINETICS AND THERMODYNAMICS STUDIES ON OIL EXTRACTION FROM SOUTHERN KADUNA PALM KERNEL SEEDS USING SUBCRITICAL WATER EXTRACTION TECHNOLOGY

Subcritical water has the potential to be highly efficient, non-toxic and low-cost alternative extraction solvent due to its unique properties under certain conditions. In this current study, we used the process variables (extraction temperature, time and particle size) to investigate the kinetics of palm kernel oil (PKO) extraction using subcritical water as solvent by considering the power law and Elovich’s kinetic law models. The laws of thermodynamics were employed to determine the spontaneity and nature of the PKO extraction process by evaluating thermodynamic parameters such as the Gibbs free energy (ΔG), enthalpy change (ΔH) and entropy change (ΔS). The experimental result showed that the conditions for the optimum yield of PKO using subcritical water were established at 0.5 mm, 120 minutes and 493K (200 ◦C) where the highest oil yield was (49.02%). The experimental data was found to best fit the power law model compared to the Elovich’s model, as a result of its highest R2 and lowest SD and RMS values. Thermodynamics analysis showed that PKO extraction has positive enthalpy and entropy values of 7.23×10-4kJ/mol and 0.0304kJ/molK respectively, indicating an endothermic and irreversible process. The negative values of Gibbs free energy (– 12.56 to -14.99kJ/molK) indicated that the extraction process is spontaneous. Gas chromatography analysis showed that lauric acid (48.1%) appears as the predominant fatty acid in the extracted oil followed by myristic acid (16.0%) and linoleic acid (14.9%). The subcritical water technology was therefore, highly recommended for the extraction of PKO due to its high potentials as shown in the high oil yield obtained. The power law model was also recommended due to the overall comparative fitness to the experimental data while the thermodynamics specifications as verified in this work were also recommended to be used for process design of PKO extraction.

The Second Law of Infodynamics: A Thermocontextual Reformulation.

Vopson and Lepadatu recently proposed the Second Law of Infodynamics. The law states that while the total entropy increases, information entropy declines over time. They state that the law has applications over a wide range of disciplines, but they leave many key questions unanswered. This article analyzes and reformulates the law based on thermocontextual interpretation (TCI). The TCI generalizes Hamiltonian mechanics by defining states and transitions thermocontextually with respect to an ambient-temperature reference state. The TCI partitions energy into exergy, which can do work on the ambient surroundings, and entropic energy with zero work potential. The TCI is further generalized here to account for a reference observer's actual knowledge. This enables partitioning exergy into accessible exergy, which is known and accessible for use, and configurational energy, which is knowable but unknown and inaccessible. The TCI is firmly based on empirically validated postulates. The Second Law of thermodynamics and its information-based analog, MaxEnt, are logically derived corollaries. Another corollary is a reformulated Second Law of Infodynamics. It states that an external agent seeks to increase its access to exergy by narrowing its information gap with a potential exergy source. The principle is key to the origin of self-replicating chemicals and life.

Considering Micro/nanostructures at the Surface of Photothermal Materials: A Game Changer in Correct Estimation of Evaporation Rate and Energy Conversion Efficiency in Interfacial Solar Vapor Generation Systems.

Interfacial solar evaporator generation (ISVG) is a new, cost-effective, and eco-friendly emerging method for water desalination. Two main criteria for evaluating ISVG performance are evaporation rate (ṁ) and solar-to-vapor conversion efficiency (η). The main challenge of the previously presented models for the estimation of ṁ and η in 2D systems is that in most cases the calculated values are beyond the theoretical limits, ṁ > 1.47 kg m-2 h-1 and η > 100%, both of which are not acceptable from the thermodynamics viewpoint. Also, the recently presented strategy of reduced vaporization enthalpy for obtaining η < 100% is unacceptable from the thermodynamics approach for ISVG as a two-step continuous process. Therefore, this work aims to present a model and consequently new equations for the correct estimation of evaporation rate and energy conversion efficiency in two-dimensional (2D)-ISVG systems, which are consistent with their corresponding theoretical limits. The basis of the present model is discrimination between the projection area and evaporation area by considering the micro/nanostructures on the surface of interfacial support (photothermal material). This leads to the presentation of new equations for ṁ and η having consistency with thermodynamics laws. The presence of micro/nanostructures on the surface of photothermal material provides a higher evaporation area which is not considered in the previous models and led to theoretically inconsistent results. The results of the present study provide a theoretical basis for the correct estimation of the evaporation rate and energy conversion efficiency in 2D-ISVG systems in future works.