Second Law Of Thermodynamics Research Articles

An elastoplastic-damage model based on nonlocal peridynamic theory for ductile damage analysis under cyclic loading

In this paper, a new thermodynamically consistent model is presented for predicting the elastoplastic-damage behavior of ductile materials using the ordinary state-based peridynamic theory. The innovative idea of this paper lies in the definition of a damage variable for each material point to simulate deterioration. By coupling the newly defined damage variable with the elastoplastic formulation, the presented peridynamic model is capable of demonstrating the initiation and evolution of damage in ductile materials subjected to cyclic loading. In this paper, the consideration of damage is based on phenomenological aspects. To capture this phenomenon, suitable state variables and corresponding thermodynamical forces are defined and isotropic and kinematic hardenings are incorporated based on the equivalent plastic stretch. By defining a dissipation potential that adheres to the requirements of the second law of thermodynamics, the presented peridynamic constitutive model achieves its purpose and the evolution laws for internal variables are derived from the defined dissipation potential. The numerical results, obtained through the employed integration algorithm, demonstrate that the presented peridynamic elastoplastic-damage model can accurately predict the initiation and growth of damage. Furthermore, the model exhibits the capability to simulate the behavior of low cycle fatigue and accurately predict material fatigue failure.

Comparative Assessment of Chloride Family Hydrogen Production Cycles Driven by a Nuclear-Geothermal Energy System

Comparative Assessment of Chloride Family Hydrogen Production Cycles Driven by a Nuclear-Geothermal Energy System

A Cosmological Model With Second Law Of Thermodynamics In F(R, T) Gravity

A Cosmological Model With Second Law Of Thermodynamics In F(R, T) Gravity

Natural validation of the second law of thermodynamics in cosmology

Natural validation of the second law of thermodynamics in cosmology

A Lagrangian Formulation for the Oldroyd B Fluid and the Second Law of Thermodynamics

A Lagrangian Formulation for the Oldroyd B Fluid and the Second Law of Thermodynamics

Quantifying Thermal Transport in Three-Dimensional Printed Fractal Structures

Abstract Heat transport through three-dimensional 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∝e−α 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.

A few remarks concerning application of the Lifshitz theory to calculation of the Casimir–Polder interaction

The Lifshitz theory provides a semiclassical description of the Casimir–Polder atom-plate interaction, where the electromagnetic field is quantized, whereas the material of the plate is considered as a continuous medium. This places certain restrictions on its application regarding the allowable atom-plate separation distances and the dielectric properties of the plate material. Below, we demonstrate that in some recent literature the application conditions of the Lifshitz theory established by its founders are violated by applying it at too short separations and using the dielectric permittivities possessing the negative imaginary parts in violation of the second law of thermodynamics.

Finite element analysis of materially uniform dielectric elastomers

In the definition of Noll, a body is uniform if all points are made of the same material. As shown by Noll himself and by Epstein and Maugin, uniformity makes the Helmholtz free energy depend on the material point exclusively through a tensor field, called uniformity tensor or implant tensor or material isomorphism. Uniformity is therefore a particular case of inhomogeneity. In turn, uniformity includes homogeneity as a particular case: indeed, homogeneity is attained when the uniformity tensor happens to be integrable. This work focuses on the non-linear large-deformation behaviour of uniform dielectric elastomers. Building on the foundational works of Toupin, Eringen and others, this work integrates continuum mechanics with electrostatics to develop a finite element framework for analysing uniform dielectric elastomers. This framework allows for considering the inherent inhomogeneity in materials exhibiting non-linear electromechanical coupling such as electro-active polymers. The inhomogeneity is assumed to be self-driven, i.e., not implied by the second law of thermodynamics: rather, it depends on the torsion of the connection (covariant derivative) induced by the uniformity tensor. A MATLAB®-based finite element solver is developed and applied to the simulation of an electromechanical beam-type actuator. The solver is robust and capable of addressing various simulation scenarios. Numerical simulations demonstrate the significant impact of material uniformity on actuator performance. This research provides a tool for future applications in dielectric elastomers, particularly in sensors, actuators and bio-inspired robotics.

Universal validity of the second law of information thermodynamics

Adiabatic measurements, followed by feedback and erasure protocols, have often been considered as a model to embody Maxwell’s Demon paradox and to study the interplay between thermodynamics and information processing. Such studies have led to the conclusion, now widely accepted in the community, that Maxwell’s Demon and the second law of thermodynamics can peacefully coexist because any gain provided by the demon must be offset by the cost of performing the measurement and resetting the demon’s memory to its initial state. Statements of this kind are collectively referred to as second laws of information thermodynamics and have recently been extended to include quantum theoretical scenarios. However, previous studies in this direction have made several assumptions, particularly about the feedback process and the demon’s memory readout, and thus arrived at statements that are not universally applicable and whose range of validity is not clear. In this work, we fill this gap by precisely characterizing the full range of quantum feedback control and erasure protocols that are overall consistent with the second law of thermodynamics. This leads us to conclude that the second law of information thermodynamics is indeed universal: it must hold for any quantum feedback control and erasure protocol, regardless of the measurement process involved, as long as the protocol is overall compatible with thermodynamics. Our comprehensive analysis not only encompasses new scenarios but also retrieves previous ones, doing so with fewer assumptions. This simplification contributes to a clearer understanding of the theory.

Studying Thermal and Dynamical Stability of Interacting Rényi and Tsallis Holographic Dark Energy Models in LTB Inhomogeneous Universe

Abstract This work aims to investigate the different stability conditions of two scenarios of the inhomogeneous Lemaitre–Tolman–Bond model of the universe with holographic dark energy. We considered the Rényi and Tsallis holographic models of interacting dark energy. These holographic models are investigated using the IR cutoff that equals the Hubble horizon. Various stability conditions of these models have been investigated to understand how much these models can tell us about the recent and future epochs of the universe in comparison with the cosmological constant model, or ΛCDM model. The conditions of violating the cosmological energy conditions have been studied. The evolution of the entropy and its first and second derivatives have been calculated and plotted for these holographic models. This gives an idea of how far these models satisfy the generalized second law of thermodynamics and hence have thermodynamical stability. The dynamical stability is studied for these evolved models, which give us glimpses of the dynamical stability at different phases of its evolution. We focus on investigating the stability in recent and near future times up to z ≤ −4. Further investigation of stability has been obtained by studying the evolved sound speed squared parameter for these models, which gave us a final and decisive evaluation of the stability of these models.

A unified physics-based continuum theory for magnetorheological fluid deformation: Implications in magnetorheological fluid-based brake applications

Magnetorheological (MR) fluids are smart composites that can exhibit reversible behavior changes and quickly transit from a liquid state to a nearly solid state when exposed to magnetic fields. Existing theories, such as the Herschel–Bulkley (H-B) model and artificial neural network, are frequently employed to describe the deformation of MR fluids; however, these are limited to certain modes of deformation and have lagged in the physical interpretation of magneto–mechanical interaction. To address the limitations, this study provides an in-depth investigation of MR fluid behavior, highlighting its non-Newtonian characteristics and the occurrence of a yielding phenomenon under finite deformation. A unified framework is developed to describe solid and fluid characteristics using classical continuum mechanics and Ericksen's seminal work consistent with the second law of thermodynamics. To highlight the distinctive characteristics of MR fluids, the investigation explores different deformation modes, including shear, flow, and squeezing. This study comprehensively addresses essential phenomena in MR fluids, including yielding, rate-dependent viscosity, and the Weissenberg effect, by leveraging the physical insights from their interaction with magnetic fields. We performed experiments with a rheometer to validate these conclusions and contrasted the analytical findings with the experimental data. Additionally, we confirmed the theoretical predictions for flow mode deformation by comparing them with existing experiments, offering a thorough explanation of field-dependent flow properties. The presented theory is also used to analyze the breaking for the MR brake system analytically, which is then validated by comparing it with the experiment. The proposed framework serves as a valuable tool for understanding and predicting the behavior of MR fluids, enabling the realization of their full potential in practical applications, such as MR fluid-based clutches and vibration dampers.

Detailed definition of temperature for nonequilibrium thermodynamics: Essential for information and quantum thermodynamics

The detailed definition of temperature has been the fundamental subject for the nonequilibrium thermodynamic theory essentially for information and quantum thermodynamic theories. The present definition of temperature is based on equilibrium thermodynamics because it is defined under the irreversible adiabatic condition using the local-equilibrium assumption. The temperature of a nonequilibrium state must be defined under the nonadiabatic condition for nature or the world. Nature is reversible in time in kinetics and phase transition. The world is irreversible in time in information and life under the second law of thermodynamics. The world is a temporal stage with an appropriate time scale upon the irreversible process of the universe with a vast time scale. The temperature in the world retaining information and life was defined under the nonadiabatic condition against that in the universe under the adiabatic condition. Information has an essential role in quantum thermodynamics through the quantum superposition principle, which enables us to carry out quantum computations.

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.

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.

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.

Foundations of algorithmic thermodynamics.

Gács's coarse-grained algorithmic entropy leverages universal computation to quantify the information content of any given physical state. Unlike the Boltzmann and Gibbs-Shannon entropies, it requires no prior commitment to macrovariables or probabilistic ensembles, rendering it applicable to settings arbitrarily far from equilibrium. For measure-preserving dynamical systems equipped with a Markovian coarse graining, we prove a number of fluctuation inequalities. These include algorithmic versions of Jarzynski's equality, Landauer's principle, and the second law of thermodynamics. In general, the algorithmic entropy determines a system's actual capacity to do work from an individual state, whereas the Gibbs-Shannon entropy gives only the mean capacity to do work from a state ensemble that is known a priori.

Universal Upper Bound on Ergotropy and No-Go Theorem by the Eigenstate Thermalization Hypothesis.

We show that the maximum extractable work (ergotropy) from a quantum many-body system is constrained by "local athermality" of an initial state and "local entropy decrease" brought about by quantum operations. The obtained universal upper bound on ergotropy implies that the eigenstate thermalization hypothesis prohibits work extraction from energy eigenstates by means of finite-time unitary operations. This no-go property implies that Planck's principle, a form of the second law of thermodynamics, holds even for pure quantum states. Our result bridges two independently studied concepts of quantum thermodynamics, the second law and thermalization, via "intrasystem" correlations in many-body systems as a resource for work extraction.

A critical review on enhancement and sustainability of energy systems: perspectives on thermo-economic and thermo-environmental analysis

Given the increased natural resource consumption of contemporary energy conversion systems, as well as the emissions, waste disposal, and climate changes that accompany them, a critical review of new techniques - known as thermo-economic and thermo-environmental analyses - has been carried out for the evaluation and optimization of energy conversion processes, from the perspectives of thermodynamics, economics, and the environment. Such a review study is essential because of the energy system’s impacts on sustainability and performance management requirements, and more importantly, it is crucial to understand the whole picture of performance evaluation of energy systems from the sustainability perspective. The study evaluated the performance and optimization of energy systems and examined the different approaches that integrate the economic, environmental, and second law of thermodynamics for sustainable development. Moreover, to assess the technical, economic, and environmental worth of energy systems and guarantee that the chosen designs are well-suited to a sustainable development framework, a mix of thermodynamic, economic, and environmental indicators is taken into consideration. In this regard, thirteen sustainability indicators for the design, analysis, and performance improvement of energy systems from the viewpoints of thermodynamics, economics, and the environment are presented and discussed. The outcome of this study shows that (i) the sustainability of energy conversion systems can be enhanced with the use of exergy techniques assessment; (ii) by reducing energy losses, exergy efficiency initiatives can lessen their adverse effects on the environment; (iii) the best methods for efficient use of energy resources, low energy production costs, and less environmental impact can be provided by hybrid energy systems; and (iv) use of a single performance metric to optimize the energy process results in improbable outcomes. Hence, multi-criteria techniques should be utilized, allowing for a more comprehensive optimization and planning of sustainable energy systems. Researchers and field engineers working on energy systems’ design, modeling, assessment, and performance optimization would find great value in this comprehensive review study.

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.