Search Results (196)

A ring of classical charge with a charged point particle oscillating within is first analyzed. The charged particle interacts with classical electromagnetic thermal radiation, which causes the particle to fluctuate, while the ring of charge imparts a resonant frequency to the particle’s motion. Oscillations in one direction within the plane of the ring are analyzed. The radius of the ring is slowly altered. The accompanying change in the particle’s average internal energy and the average work done in changing the radius are calculated. This leads to a derivation of the classical electromagnetic zero-point radiation spectrum. Next, the second law of thermodynamics is applied to the entropy to enable a more general derivation of the Wien displacement law. With this derivation, zero-point radiation can be included in the Wien displacement law. Finally the definition of the thermodynamic temperature is emphasized, and methods for performing the needed calculations for the temperature ratio are discussed. Full article

Modified gravity theories with a nonminimal coupling between curvature and matter offer a compelling alternative to dark energy and dark matter by introducing an explicit interaction between matter and curvature invariants. Two of the main consequences of such an interaction are the emergence of an additional force and the non-conservation of the energy–momentum tensor, which can be interpreted as an energy exchange between matter and geometry. By adopting this interpretation, one can then take advantage of many different approaches in order to investigate the phenomenon of gravitationally induced particle creation. One of these approaches relies on the so-called irreversible thermodynamics of open systems formalism. By considering the scalar–tensor formulation of one of these theories, we derive the corresponding particle creation rate, creation pressure, and entropy production, demonstrating that irreversible particle creation can drive a late-time de Sitter acceleration through a negative creation pressure, providing a natural alternative to the cosmological constant. Furthermore, we demonstrate that the generalized second law of thermodynamics holds: the total entropy, from both the apparent horizon and enclosed matter, increases monotonically and saturates in the de Sitter phase, imposing constraints on the allowed particle production dynamics. Furthermore, we present brief reviews of other theoretical descriptions of matter creation processes. Specifically, we consider approaches based on the Boltzmann equation and quantum-based aspects and discuss the generalization of the Klein–Gordon equation, as well as the problem of its quantization in time-varying gravitational fields. Hence, gravitational theories with nonminimal curvature–matter couplings present a unified and testable framework, connecting high-energy gravitational physics with cosmological evolution and, possibly, quantum gravity, while remaining consistent with local tests through suitable coupling functions and screening mechanisms. Full article

At present, enhancing the first- and second-law efficiencies of power generation cycles is no longer the sole objective of engineers. Increasing attention is now being paid to reducing carbon emissions in the environment and minimizing the time required to recover the costs of the power plant, in addition to improving work output and first- and second-law efficiencies. The present analytical study compares the power generation cycle with and without a carbon capture unit. The combined cycle selected is the reheat gas turbine cycle using an ammonia–water mixture and transcritical carbon dioxide as working fluids in the bottoming cycle. The comparison of both the configurations depicts that at a cycle pressure ratio of 40, an ambient temperature of 303 K, and a turbine inlet temperature of 1600 K, the configuration incorporating the maximum number of ammonia–water turbines in the bottoming cycle yields the highest work output, amounting to 952.3 kJ/kg. The payback period is found to be the longest—approximately 8 years and 4 months for the configuration utilizing transcritical carbon dioxide as the working fluid. The integration of a carbon capture unit results in a reduction in carbon emissions ranging from a minimum of 15% to a maximum of 22.81%. However, a higher operating separation temperature for ammonia and water is observed to degrade the thermodynamic performance across all configurations analyzed. Full article

The dynamics of port-Hamiltonian systems is based on energy balance principles (the first law of thermodynamics) embedded in the structure of the model. However, when dealing with thermodynamic subsystems, the second law (entropy production) should also be explicitly taken into account. Several frameworks were developed as extensions to the thermodynamic domain of port-Hamiltonian systems. In our work, we study three of them, namely irreversible port-Hamiltonian systems, entropy-based generalized Hamiltonian systems, and entropy-production-metric-based port-Hamiltonian systems, which represent alternative approaches of selecting the state variables, the storage function, simplicity of physical interpretation, etc. On the example of a simplified lumped-parameter model of a heat exchanger, we study the frameworks in terms of their implementability for an IDA-PBC-like control and the simplicity of using these frameworks for practitioners already familiar with the port-Hamiltonian systems. The comparative study demonstrated the possibility of using each of these approaches to derive IDA-PBC-like thermodynamically consistent control and provided insight into the applicability of each framework for the modeling and control of multiphysics systems with thermodynamic subsystems. Full article

We present a model of superfluidity based on the internal variable theory. We consider a two-component fluid endowed with a scalar internal variable whose gradient is the counterflow velocity. The restrictions imposed by the second law of thermodynamics are obtained by applying a generalized Coleman–Noll procedure. A set of constitutive equations of the Landau type, with entropy, entropy flux and stress tensor depending on the counterflow velocity, is obtained. The propagation of acceleration waves is investigated as well. It is shown that the first-and-second sound waves may propagate along the system with speeds depending on the physical parameters of the two fluids. First sound waves may propagate in the same direction or in the opposite direction of the counterflow velocity, depending on the concentration of normal and superfluid components. The speeds of second sound waves have the same mathematical form of those propagating in dielectric crystals. Full article

There is much confusion about the apparent opposition between Darwinian evolution and the second law of thermodynamics. Both entropy and entropy production play more fundamental roles in the origin of life and Darwinian evolution than is generally recognized. I argue that Darwinian evolution can be understood as a tendency for entropy production to increase. Since the second law is about the increase in entropy, this hypothesis goes beyond the second law because it is about the increase in entropy production. This hypothesis can explain some aspects of biology that Darwinism struggles with, such as the origin of life, the origin of Darwinism, ecological successions, and an apparent general trend towards biological complexity. Gould proposed a wall of minimal complexity to explain this apparent increase in biological complexity. I argue that the apparent increase in biological complexity can be understood as a tendency for biological entropy production to increase through a broader range of free energy transduction mechanisms. In the context of a simple universe-in-a-cup-of-coffee model, entropy production is proposed as a more quantifiable replacement for the notion of complexity. Finally, I sketch the cosmic history of entropy production, which suggests that increases and decreases of free energy availability constrain the tendency for entropy production to increase. Full article

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

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

Clouds play a central role in regulating incoming solar radiation and outgoing terrestrial emission; hence, they must be internally constrained to prognose Earth’s temperature. At the same time, planetary fluids are inherently turbulent, so the climate state would tend toward maximum entropy production—a generalized second law of thermodynamics. Incorporating these requirements, I have previously formulated an aquaplanet model to demonstrate that intrinsic water properties may strongly lower the climate sensitivity to solar irradiance, thereby resolving the faint young Sun paradox (FYSP). In this paper, I extend the model to include other external forcings and show that sensitivity to the reduced outgoing longwave radiation by the elevated pCO₂ can be several times greater, but the global temperature remains capped at ~40 °C by the exponential increase in saturated vapor pressure. I further show that planetary albedo augmented by a tropical supercontinent may cool the climate sufficiently to cause tropical glaciation. And since the glacial edge is marked by above-freezing temperature, it abuts an open, co-zonal ocean, thereby obviating the “Snowball Earth” hypothesis. Our theory thus provides a unified framework for interpreting Earth’s diverse climates, including the FYSP, the warm extremes of the Cambrian and Cretaceous, and the tropical glaciations of the Precambrian. Full article

This paper revisits some aspects connected with the methods for the determination of thermodynamically consistent models. While the concepts apply to the general context of continuum physics, the details are developed for the modelling of deformable dielectrics. The symmetry condition arising from the balance of angular momentum is viewed as a constraint for the constitutive equations and is shown to be satisfied by sets of objective fields that account jointly for deformation and electric field. The second law of thermodynamics is considered in a generalized form where the entropy production is given by a constitutive function possibly independent of the other constitutive functions. Furthermore, a representation formula is applied for solving the Clausius–Duhem inequality with respect to the chosen unknown fields. Full article

Fluid flow along an inclined channel phenomenon is crucial in several geophysical, environmental, engineering, biological, and industrial processes, and in aerodynamics and hemodynamics. This present study examines the effect of a constant magnetic field on the entropy production rate in a steady flow of Casson fluid along an inclined heated channel. The governing equations for the flow of velocity, temperature, and entropy generation are formulated based on the Casson constitutive relations and thermodynamics’ first and second laws. The exact solutions are constructed for the dimensionless equations and validated with previous results in the literature. The effects of various fluid parameters on the flow, heat transfer, and entropy production rate are conducted and reported graphically with adequate discussion. The impact of the Hartmann number parameter reveals a decrease in both flow velocity and entropy generation rate, meanwhile it also enhances the fluid temperature distribution across the inclined channel. An opposite trend is, however, observed with the Casson fluid parameter. Full article

We investigate the thermodynamic compatibility of weakly nonlocal materials with constitutive equations depending on the third spatial gradient of the deformation and the heat flux ruled by an independent balance law. In such materials, the molecules experience long-range interactions. Examples of biological systems undergoing nonlocal interactions are given. Under the hypothesis of weak nonlocality (constitutive equations depending on the gradients of the unknown fields), we exploit the second law of thermodynamics by considering the spatial differential consequences (gradients) of the balance laws as additional equations to be substituted into the entropy inequality, up to the order of the gradients entering the state space. As a consequence of such a procedure, we obtain generalized constitutive laws for the stress tensor and the specific entropy, as well as new forms of the balance equations. Such equations are, in general, parabolic, although hyperbolic situations are also possible. For small deformations of homogeneous and isotropic bodies, under the validity of a generalized Maxwell–Cattaneo equation for the heat flux, which depends on the deformation too, we study the propagation of small-amplitude thermomechanical waves, proving that mechanical, thermal and thermomechanical waves are possible. Full article

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. Full article

A marble processing plant (MPP) can achieve sustainable development by implementing energy-saving and consumption-reduction technology. Reducing energy loss in such an energy-intensive plant is crucial for overall energy savings. This study establishes an MPP optimization model based on the second law of thermodynamics and the law of conservation of mass. Marble is an aesthetically pleasing and long-lasting building material that has boosted economies in European and sub-Saharan African nations. However, high energy costs and scarcity have constrained the industry’s economic potential and hindered the achievement of optimal levels of production. The second law of thermodynamics is adopted to study the irreversibilities, inefficiencies, and exergetic performance of a marble processing plant. The Aspen Plus commercial software application is used to model and generate thermodynamic data, determine energy flow streams and conduct sensitivity and optimization analysis to improve data quality and energetic performance outcomes. From the results, the various scales of the exergetic destruction, efficiencies, and exergetic losses are determined, and recommendations are established. The overall energy and exergy efficiency levels were determined to be 87.43% and 86.84%, respectively, with a total exergetic destruction of 200.61 kW. The reported methodologies, cutting-edge ideas, and solutions will give industrialists and other significant stakeholders in the global manufacturing sector cutting-edge information about energy usage and ways to cut energy losses in both new and existing factory designs, manage energy cost components, and adjust energy efficiency to maximize productivity. Full article