Search Results (192)

In a world increasingly dependent on digital computers, understanding the relationship between information theory and thermodynamics is essential. A recent attempt to address this issue was made by A. De Vos who, using a reversible model within the framework of finite-time thermodynamics, derived Carnot’s law, Landauer’s principle, Ohm’s law, and even Moore’s law. Following De Vos et al., this paper first recovers the efficiency of Curzon and Ahlborn, and then establishes the so-called endoreversible Landauer principle for a traditional computer gate, assuming the gate operates in the Maximum Power regime. However, two other regimes are particularly important: the Omega function and the Efficient Power function. By considering these, we obtain the corresponding thermodynamic efficiencies and compare them against that of the Maximum Power regime. Full article

This paper presents a theoretical optimization of an endoreversible compressor under steady-state conditions. A parametric study using finite-time thermodynamic principles highlights the effect of external irreversibilities on compressor performance. A compressor efficiency metric is established based on heat pump theory’s analogous performance coefficient concept. The external irreversibilities are characterized as functions of the conductance coefficients between the compressor and the low- and high-pressure reservoirs. In particular, the influence of suction and discharge tube diameters and gas pressures is investigated to determine the optimum compressor operating performance for a given gas mass flow rate. The results highlight the importance of selecting optimal suction and discharge tube diameters to improve compressor power efficiency and minimize energy consumption during gas compression. Full article

In celebration of 50 years of the endoreversible Carnot-like heat engine, this work aims to link the thermodynamic success of the irreversible Carnot-like heat engine with the stability dynamics of the engine. This region of success is defined by two extreme configurations in the interaction between heat reservoirs and the working fluid. The first corresponds to a fully reversible limit, and the second one is the fully dissipative limit; in between both limits, the heat exchange between reservoirs and working fluid produces irreversibilities and entropy generation. The distance between these two extremal configurations is minimized, independently of the chosen metric, in the state where the efficiency is half the Carnot efficiency. This boundary encloses the region where irreversibilities dominate or the reversible behavior dominates (region of success). A general stability dynamics is proposed based on the endoreversible nature of the model and the operation parameter in charge of defining the operation regime. For this purpose, the maximum ecological and maximum Omega regimes are considered. The results show that for single perturbations, the dynamics rapidly directs the system towards the success region, and under random perturbations producing stochastic trajectories, the system remains always in this region. The results are contrasted with the case in which no restitution dynamics exist. It is shown that stability allows the system to depart from the original steady state to other states that enhance the system’s performance, which could favor the evolution and specialization of systems in nature and in artificial devices. Full article

Finite-time thermodynamics (FTT) describes the study of thermodynamic processes that take place in finite time. Due to the finite-time requirement, in general the system cannot move from equilibrium state to equilibrium state. As a consequence, excess entropy is generated, available work is reduced, and/or the maximally achievable efficiency is not achieved; minimizing these negative side-effects constitutes an optimal control problem. Particularly challenging are processes and cycles that involve phase transitions of the working fluid material or the target material of a synthesis process, especially since most materials reside on a highly complex energy landscape exhibiting alternative metastable phases or glassy states. In this perspective, we discuss the issues and challenges involved in dealing with such materials when performing thermodynamic processes that include phase transitions in finite time. We focus on thermodynamic cycles with one back-and-forth transition and the generation of new materials via a phase transition; other systems discussed concern the computation of free energy differences and the general applicability of FTT to systems outside the realm of chemistry and physics that exhibit cost function landscapes with phase transition-like dynamics. Full article

Maintaining the required relative humidity values in the vehicle cabin is an important HVAC task, along with considerations related to the temperature, velocity, air pressure and noise. Deviation from the optimal values worsens the psycho-physiological state of the driver and affects the energy efficiency of the train. In this study, a model of liquid film formation on and removal from various cabin surfaces was constructed using the fundamental Navier–Stokes hydrodynamic equations. A special transport model based on the liquid vapor diffusion equation was used to simulate the air environment inside the cabin. The evaporation and condensation of surface films were simulated using the Euler film model, which directly considers liquid–gas and gas–liquid transitions. Numerical results were obtained using the RANS equations and a turbulence model by means of the finite volume method in Ansys CFD. Conjugate fields of temperature, velocity and moisture concentration were constructed for various time intervals, and the dependence values for the film thicknesses on various surfaces relative to time were determined. The verification was conducted in comparison with the experimental data, based on the protocol for measuring the microclimate indicators in workplaces, as applied to the train cabin: the average ranges encompassed temperature changes from 11% to 18%, and relative humidity ranges from 16% to 26%. Comparison with the results of other studies, without considering the phase transition and condensation, shows that, for the warm mode, the average air temperature in the cabin with condensation is 12.5% lower than without condensation, which is related to the process of liquid evaporation from the heated walls. The difference in temperature values for the model with and without condensation ranged from −12.5% to +4.9%. We demonstrate that, with an effective mode of removing condensate film from the window surface, including recirculation modes, the energy consumption of the climate control system improves significantly, but this requires a more accurate consideration of thermodynamic parameters and relative humidity. Thus, considering the moisture condensation model reveals that this variable can significantly affect other parameters of the microclimate in cabins: in particular, the temperature. This means that it should be considered in the numerical modeling, along with the basic heat transfer equations. Full article

Endoreversible engine cycles are a cornerstone of finite-time thermodynamics. We show that endoreversible Stirling engines operating with a one-component plasma as a working medium run at maximal power output with the Curzon–Ahlborn efficiency. As a main result, we elucidate that this is actually a consequence of the fact that the caloric equation of state depends only linearly on temperature and only additively on volume. In particular, neither the exact form of the mechanical equation of state nor the full fundamental relation are required. Thus, our findings immediately generalize to a larger class of working plasmas, far beyond simple ideal gases. In addition, we show that for plasmas described by the photonic equation of state, the efficiency is significantly lower. This is in stark contrast to endoreversible Otto cycles, for which photonic engines have an efficiency larger than the Curzon–Ahlborn efficiency. Full article

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

In this manuscript, the typical problems of “finite-time thermodynamics”, their general methodology, and the general features of their solutions are considered. We also consider the role of minimal dissipation processes, the properties of the irreversibility index, and the consequences of its existence. A generalization of the Carathéodory theorem for averaged optimization problems corresponding to cyclic processes and the properties of optimal solutions following from it are given. The existence of the irreversibility index for economic macrosystems and their analogies to and differences from thermodynamic systems are proven. Full article

The provision of food in pre-Inca/Inca cultures (1000 BC–≈1532 AD) in environments near Lake Titikaka (approximately 4000 m above sea level) was possible through an agricultural technique called “Waru-Waru”, which consists of filling the space (volume) between rows of land containing plants that are cultivated (a series of earth platforms surrounded by water canals) with water, using water as thermal energy storage to store energy during the day and to regulate the temperature of the soil and crop atmosphere at night. The problem is that these cultures left no evidence in written documents that have been preserved to this day indicating the mathematical models, the physics involved, and the experimental part they performed for the research, development, and innovation of the “Waru-Waru” technique. From a review of the existing literature, there is (1) bibliography that is devoted to descriptive research (about the geometry, dimensions, and shapes of the crop fields (and more based on archaeological remains that have survived to the present day) and (2) studies presenting complex mathematical models with many physical parameters measured only with recently developed instrumentation. The research objectives of this paper are as follows: (1) develop a mathematical model that uses finite differences in fluid mechanics, thermodynamics, and heat transfer to explain the experimental and theory principles of this pre-Inca/Inca technique; (2) the proposed mathematical model must be in accordance with the mathematical calculation tools available in pre-Inca/Inca cultures (yupana and quipu), which are mainly based on arithmetic operations such as addition, subtraction, and multiplication; (3) develop a mathematical model in a sequence of steps aimed at determining the best geometric form for thermal energy storage and plant cultivation and that has a simple design (easy to transmit between farmers); (4) consider the assumptions necessary for the development of the mathematical model from the point of view of research on the geometry of earth platforms and water channels and their implantation in each cultivation area; (5) transmit knowledge of the construction and maintenance of “Waru-Waru” agricultural technology to farmers who have cultivated these fields since pre-Hispanic times. The main conclusion is that, in the mathematical model developed, algebraic mathematical expressions based on addition and multiplication are obtained to predict and explain the evolution of soil and water temperatures in a specific crop field using crop field characterization parameters for which their values are experimentally determined in the crop area where a “Waru-Waru” is to be built. Therefore, the storage of thermal energy in water allows crops to survive nights with low temperatures, and indirectly, it allows the interpretation that the Inca culture possessed knowledge of mathematics (addition, subtraction, multiplication, finite differences, approximation methods, and the like), physics (fluids, thermodynamics, and heat transfer), and experimentation, with priority given to agricultural techniques (and in general, as observed in all archaeological evidence) that are in-depth, exact, practical, lasting, and easy to transmit. Understanding this sustainable energy storage technique can be useful in the current circumstances of global warming and climate change within the same growing areas and/or in similar climatic and environmental scenarios. This technique can help in reducing the use of fossil or traditional fuels and infrastructure (greenhouses) that generate heat, expanding the agricultural frontier. Full article

We survey developments in the use of entropy maximization for applying the Gibbs Canonical Ensemble to finite situations. Biological insights are invoked along with physical considerations. In the game-theoretic approach to entropy maximization, the interpretation of the two player roles as predator and prey provides a well-justified and symmetric analysis. The main focus is placed on the Lagrange multiplier approach. Using natural physical units with Planck’s constant set to unity, it is recognized that energy has the dimensions of inverse time. Thus, the conjugate Lagrange multiplier, traditionally related to absolute temperature, is now taken with time units and oriented to follow the Arrow of Time. In quantum optics, where energy levels are bounded above and below, artificial singularities involving negative temperatures are eliminated. In a biological model where species compete in an environment with a fixed carrying capacity, use of the Canonical Ensemble solves an instance of Eigen’s phenomenological rate equations. The Lagrange multiplier emerges as a statistical measure of the ecological age. Adding a weak inequality on an order parameter for the entropy maximization, the phase transition from initial unconstrained growth to constrained growth at the carrying capacity is described, without recourse to a thermodynamic limit for the finite system. Full article

The application of ceramic particle-reinforced metal matrix composites (CPRMMCs) in the nuclear power sector is primarily dependent on their mechanical and thermal properties. A comprehensive understanding of the structure–property (SP) linkages between microstructures and macroscopic properties is critical for optimizing material properties. However, traditional studies on SP linkages generally rely on experimental methods, theoretical analysis, and numerical simulations, which are often associated with high time and economic costs. To address this challenge, this study proposes a novel method based on Materials Informatics (MI), combining the finite element method (FEM), graph Fourier transform, principal component analysis (PCA), and machine learning models to establish the SP linkages between the microstructure and thermodynamic properties of CPRMMCs. Specifically, FEM is used to model the microstructures of CPRMMCs with varying particle volume fractions and sizes, and their elastic modulus, thermal conductivity, and coefficient of thermal expansion are computed. Next, the statistical features of the microstructure are captured using graph Fourier transform based on two-point spatial correlations, and PCA is applied to reduce dimensionality and extract key features. Finally, a polynomial kernel support vector regression (Poly-SVR) model optimized by Bayesian methods is employed to establish the nonlinear relationship between the microstructure and thermodynamic properties. The results show that this method can effectively predict FEM results using only 5–6 microstructure features, with the R² values exceeding 0.91 for the prediction of thermodynamic properties. This study provides a promising approach for accelerating the innovation and design optimization of CPRMMCs. Full article

When developing deep subsurface infrastructure in areas with intense geothermal activity, the significant temperature gradient inevitably leads to low-temperature contraction and high-temperature expansion of the rock body, resulting in changes in the rock’s mechanical properties. These thermodynamic effects can easily lead to the destabilization and subsequent collapse of the rock. There exists a pressing necessity to methodically evaluate the surrounding rock stability encountered in deep underground engineering under the action of thermal-solid coupling. This study constructed a multi-physical field coupling nonlinear calculation model based on a high-precision three-dimensional finite difference method, systematically analyzed the interdependent effects between the original rock temperature and excavation-induced disturbance, and then analyzed the dynamic changes in temperature, stress, and displacement fields along with plastic zone of surrounding rock of the deep underground engineering under thermal-solid coupling. The results indicate that the closer to the excavation contour surface, the lower the surrounding rock temperature, while the temperature gradient increased correspondingly. The farther away from the excavation contour face, the closer the temperature was to the original rock temperature. As the original rock temperature climbed from 30 °C to 90 °C, the increment of vault displacement was 2.45 times that of arch bottom displacement, and the influence of temperature change on vault deformation was more significant. The horizontal displacement magnitudes at the different original temperatures followed the following order: sidewall > spandrel > skewback, and at an original rock temperature of 90 °C, the sidewall horizontal displacement reached 15.31 cm. With the elevation of the original rock temperature, the distribution range and concentration degree of the maximum and minimum principal stresses increased obviously, and both were compression-dominated. The types of plastic zones in the surrounding rock were mainly characterized by shear stress-induced yielding and tensile stress-induced damage failure. When the original rock temperature increased to 90 °C, the rock mass extending up to 1.5 m from the excavation contour surface formed a large area of damage zone. The closer the working face was to the monitoring section, the faster the temperature dropped, and the displacement changed in the monitoring section. The findings offer a theoretical basis for engineering practice, and it is of great significance to ensure the safety of the project. Full article

Many argue that the standard understanding of the second law of thermodynamics combined with the supposition, backed by recent scientific evidence, that the future is infinite entails that one is, most likely, a momentary Boltzmann brain that will quickly disintegrate into the cosmos. The argument is as follows: (1) Given infinite time, the universe will eventually reach thermodynamic equilibrium; (2) once there, every possible fluctuation away from equilibrium, no matter how improbable, will recur, ad infinitum; (3) those fluctuations that create stable, long-lived creatures, such as we take ourselves to be, will be extremely rare compared to those that create short-lived brains that mistakenly think they are ordinary human beings; hence, by statistical reasoning, (4) one is, with overwhelming probability, just a fleeting instantiation of experience. I argue that this reasoning is invalid since it rests on an error regarding the relationship between infinite sets and their subsets. Once this error is eliminated, the power of the argument fades, and the evidence that we are ordinary human beings becomes decisive. Surprisingly, I find that the best argument for the Boltzmann brain hypothesis requires the assumption that the future is very long but finite. Full article

The significance of the chiral symmetry restoration is studied by considering the role of the modification of the nucleon mass in nuclear medium at finite density and temperature. Using the Korea-IBS-Daegu-SKKU density functional theory, we can create models that have an identical nuclear matter equation of state but different isoscalar and isovector effective masses at zero temperature. The effect of the effective mass becomes transparent at non-zero temperatures, and it becomes more important as temperature increases. The role of the effective mass is examined thoroughly by calculating the dependence of thermodynamic variables such as free energy, internal energy, entropy, pressure and chemical potential on density, temperature and proton fraction. We find that sensitivity to the isoscalar effective mass is several times larger than that of the isovector effective mass, so the uncertainties arising from the effective mass are dominated by the isoscalar effective mass. In the analysis of the relative uncertainty, we obtain that the maximum uncertainty is less than 2% for free energy, internal energy and chemical potential, but it amounts to 20% for pressure. Entropy shows a behavior completely different from the other four variables that the uncertainty is about 40% at the saturation density and increases monotonically as density increases. The effect of the uncertainty to properties of physical systems is investigated with the proto-neutron star. It is shown that temperature depends strongly on the effective mass at a given density, and substantial swelling of the radius occurs due to the finite temperature. The equation of state is stiffer with smaller isoscalar effective mass, so the effect of the effective mass appears clearly in the mass–radius relation of the proto-neutron star, where a larger radius corresponds to a smaller effective mass. Full article

Curzon and Ahlborn’s 1975 paper, a pioneering work that inspired the birth of the field of finite-time thermodynamics, unveiled the efficiency at maximum power (EMP) of the endoreversible Carnot heat engine, now commonly referred to as the Curzon–Ahlborn (CA) engine. Historically, despite the significance of the CA engine, similar findings had emerged at an earlier time, such as the Yvon engine proposed by J. Yvon in 1955 that shares the exact same EMP, that is, the CA efficiency ${\eta }_{\mathrm{CA}}$. However, the special setup of the Yvon engine has circumscribed its broader influence. This paper extends the Yvon engine model to achieve a level of generality comparable to that of the CA engine. With the power expression of the extended Yvon engine, we directly explain the universality that ${\eta }_{\mathrm{CA}}$ is independent of the heat transfer coefficients between the working substance and the heat reservoirs. A rigorous comparison reveals that the extended Yvon engine and CA engine represent the steady-state and cyclic forms of the endoreversible Carnot heat engine, respectively, and are equivalent. Full article