Minimum Entropy Production Research Articles

SIMULATION OF AGGREGATION PROCESS IN CERIUM AND ZIRCONIUM DIOXIDE NANOPARTICLES

A study of the aggregative stability of the CeO2-ZrO2 system was carried out in various pH ranges of the medium. To create a mathematical model of the stability of aggregates, the generalized DLVO theory was taken. The parameters of the structural component of the potential energy of particle interaction are determined using the principle of minimum entropy production. The limiting particle sizes of an an aggregatively stable system are determined.

Validity of Prigogine’ s minimum entropy production principle for a rigid heat-conducting solid beyond the Fourier heat transport regime

Validity of Prigogine’ s minimum entropy production principle for a rigid heat-conducting solid beyond the Fourier heat transport regime

Analysis of Energy Loss Characteristics of Vertical Axial Flow Pump Based on Entropy Production Method under Partial Conditions.

The energy loss of the vertical axial flow pump device increases due to the unstable internal flow, which reduces the efficiency of the pump device and increases its energy consumption of the pump device. The research results of the flow loss characteristics of the total internal conduit are still unclear. Therefore, to show the internal energy loss mechanism of the axial flow pump, this paper used the entropy production method to calculate the energy loss of the total conduit of the pump device to clarify the internal energy loss mechanism of the pump device. The results show that the energy loss of the impeller is the largest under various flow conditions, accounting for more than 40% of the total energy loss of the pump device. The variation trend of the volume average entropy production and the energy loss is similar under various flow coefficients (KQ). The volume average entropy production rate (EPR) and the energy loss decrease first and then increase with the increase of flow, the minimum volume average entropy production is 378,000 W/m3 at KQ = 0.52, and the area average EPR of the impeller increases gradually with the increase of flow. Under various flow coefficient KQ, the energy loss of campaniform inlet conduit is the smallest, accounting for less than 1% of the total energy loss. Its maximum value is 63.58 W. The energy loss of the guide vane and elbow increases with the increase of flow coefficient KQ, and the maximum ratio of energy loss to the total energy loss of the pump device is 29% and 21%, respectively, at small flow condition KQ = 0.38. The energy loss of straight outlet conduit reduces first and then increases with the increase of flow coefficient KQ. When flow coefficient KQ = 0.62, it accounts for 27% of the total energy loss of the pump device, but its area average entropy production rate (EPR) and volume average entropy production rate (EPR) are small. The main entropy production loss in the pump device is dominated by entropy production by turbulent dissipation (EPTD), and the proportion of entropy production by direct dissipation (EPDD) is the smallest.

Geometric conditions for minimizing entropy production in thermocouple design

This work shows a methodology for designing thermocouples of thermoelectric modules. The main quantities for design calculations are the geometric parameters: Cross-sectional area and leg length. Furthermore, the thickness of the ceramic material and the thickness of the metal bridge are considered. In addition, temperature-dependent thermoelectric properties are included in the analysis: Seebeck coefficient, thermal conductivity, electrical resistivity. An analysis of the entropy production is performed for two thermocouple geometries: Quadrangular and cylindrical. The proposed methodology allows determining the geometric conditions that the thermocouple must meet to minimize the entropy production and maximize efficiency. A conclusive result of this work is that the geometric conditions that minimize entropy production are the same that maximize the efficiency.

Linear stochastic thermodynamics

We study the thermodynamics of open systems weakly driven out-of-equilibrium by nonconservative and time-dependent forces using the linear regime of stochastic thermodynamics. We make use of conservation laws to identify the potential and nonconservative components of the forces. This allows us to formulate a unified near-equilibrium thermodynamics. For nonequilibrium steady states, we obtain an Onsager theory ensuring nonsingular response matrices that is consistent with phenomenological linear irreversible thermodynamics. For time-dependent driving protocols that do not produce nonconservative forces, we identify the equilibrium ensemble from which Green–Kubo relations are recovered. For arbitrary periodic drivings, the averaged entropy production (EP) is expressed as an independent sum over each driving frequency of non-negative contributions. These contributions are bilinear in the nonconservative and conservative forces and involve a novel generalized Onsager matrix that is symmetric. In the most general case of arbitrary time-dependent drivings, we advance a novel decomposition of the EP rate into two non-negative contributions—one solely due to nonconservative forces and the other solely due to deviation from the instantaneous steady-state—directly implying a minimum EP principle close to equilibrium. This setting reveals the geometric structure of near-equilibrium thermodynamics and generalizes previous approaches to cases with nonconservative forces.

Optimization of Power and Thermal Management System of Hypersonic Vehicle with Finite Heat Sink of Fuel

The scramjet of hypersonic vehicles faces severe high-temperature challenges, but the heat sink available for scramjet cooling is extremely finite. It is necessary to optimize its power and thermal management system (PTMS) with a finite heat sink of hydrocarbon fuel. This paper proposes a two-level optimization method for the PTMS of hypersonic vehicles at Mach 6. The PTMS is based on a supercritical carbon dioxide (SCO2) closed Brayton cycle, and its heat sink is airborne hydrocarbon fuel. System-level optimization aims to obtain the optimal system parameters for the PTMS. The minimum fuel weight penalty and the minimum heat sink consumption of fuel are the optimization objectives. The segmental (SEG) method is used to analyze the internal temperature distribution of fuel–SCO2 heat exchangers in the system-level optimal solution set. This ensures the selected optimal solutions meet the requirement of a pinch temperature difference greater than or equal to 10 °C. Further, the component-level optimization for the fuel–SCO2 heat exchanger is carried out based on the selected optimal solutions. The lightest weight of the heat exchanger and the minimum entropy production are the optimization objectives in this step. Finally, the optimal system parameters and the optimal key component parameters can be searched using this presented two-level optimization method.

Development and validation of a variational formulation of Two-Phase flow distribution

Nonuniform flow distribution in vertical headers has been an ongoing challenge that limits the advantages of transfer and fluidic technologies, especially in microchannel heat exchangers (MCHXs). This issue has been typically addressed in empirical studies and case-specific computational fluid dynamics (CFD) simulations; however, efforts toward the theoretical understanding and modeling of this phenomenon are lacking in literature. Therefore, this paper presents the development and validation of a theoretical model to reproduce the flow and phase distributions in adiabatic multibranch channels. A variational formulation of the phenomenon is obtained using Prigogine's theorem of minimum entropy production to cope with the inherent high variability of the mathematical problem. The individual flow rates, vapor quality, and pressure distributions yielding the minimum entropy generation rate provide a complete representation of the steady-state fluidic network for an arbitrary structure of the device and any working fluid. This paper presents a first experimental validation of the model when applied to the vertical header of a MCHX circulating R410A refrigerant. The theoretical results provide a coherent representation of the experimental data.

Reinforcement learning approach to shortcuts between thermodynamic states with minimum entropy production.

We propose a systematic method based on reinforcement learning (RL) techniques to find the optimal path to minimize the total entropy production between two equilibrium states of open systems at the same temperature in a given fixed period. Benefiting from the generalization of the deep RL techniques, we provide a powerful tool to address this problem in quantum systems even with two-dimensional continuous controllable parameters. We successfully apply our method to the classical and quantum two-level systems.

Critical current and loss character of quasi-isotropic strands with resistance

A quasi-isotropic strand has a central rotational symmetry structure which shows good isotropic performance on magnetization loss when the strand is subjected to an externally applied alternating magnetic field in various directions. This paper studies the critical current and ac loss character of quasi-isotropic strands by considering the resistance between tapes based on the minimum electromagnetic entropy production method. The quasi-isotropic strands show resistance dependence on critical current, transport loss, and magnetization loss. The resistance between tapes can increase the critical current without significant increases in the total loss. High-frequency excitation conditions do not increase the loss per cycle either. The results indicate that quasi-isotropic strands are highly suitable for power cables and other high-power applications.

Making Waves: A sea change in treating wastewater – Why thermodynamics supports resource recovery and recycling

Entropy is a concept defined by the second law of thermodynamics. Applying this concept to the world we live in, entropy production must be minimized and negentropy (negative entropy production) should be accelerated, in order to produce a healthy and stable ecological system. The present wastewater treatment, however, contributes to entropy production. This means that conventional wastewater treatment, without recovery of resource and energy, will gradually but inevitably contribute to a deteriorating ecological balance. When the self-cleaning ability of the natural ecological system is limited, the need to develop sustainable wastewater treatment in order to delay entropy production and accelerate negentropy becomes urgent. Resource and energy recovery from wastewater should be the first priority, as they can contribute significantly towards minimizing entropy production and accelerating negentropy. Sustainable wastewater treatment must focus on recovering recyclable high value-added organic chemicals from wastewater and/or excess sludge to minimize entropy production caused by methane (CH4, once combusted, is converted into CO2 - an even higher substance in entropy) via anaerobic digestion. Instead of CH4, thermal energy present in the effluent can be utilized for heating/cooling buildings and also for drying excess sludge towards incineration to recover more energy. Overall, this can lead to a carbon-neutral operation and even creating a “carbon sink” could be possible for wastewater treatment.

Complexity and efficiency of minimum entropy production probability paths from quantum dynamical evolutions.

We present an information geometric characterization of quantum driving schemes specified by su(2;C) time-dependent Hamiltonians in terms of both complexity and efficiency concepts. Specifically, starting from pure output quantum states describing the evolution of a spin-1/2 particle in an external time-dependent magnetic field, we consider the probability paths emerging from the parametrized squared probability amplitudes of quantum origin. The information manifold of such paths is equipped with a Riemannian metrization specified by the Fisher information evaluated along the parametrized squared probability amplitudes. By employing a minimum action principle, the optimum path connecting initial and final states on the manifold in finite time is the geodesic path between the two states. In particular, the total entropy production that occurs during the transfer is minimized along these optimum paths. For each optimum path that emerges from the given quantum driving scheme, we evaluate the so-called information geometric complexity (IGC) and our newly proposed measure of entropic efficiency constructed in terms of the constant entropy production rates that specify the entropy minimizing paths being compared. From our analytical estimates of complexity and efficiency, we provide a relative ranking among the driving schemes being investigated. Moreover, we determine that the efficiency and the temporal rate of change of the IGC are monotonic decreasing and increasing functions, respectively, of the constant entropic speed along these optimum paths. Then, after discussing the connection between thermodynamic length and IGC in the physical scenarios being analyzed, we briefly examine the link between IGC and entropy production rate. Finally, we conclude by commenting on the fact that an higher entropic speed in quantum transfer processes seems to necessarily go along with a lower entropic efficiency together with a higher information geometric complexity.

Minimum entropy production, detailed balance and Wasserstein distance for continuous-time Markov processes

We investigate the problem of minimizing the entropy production for a physical process that can be described in terms of a Markov jump dynamics. We show that, without any further constraints, a given time-evolution may be realized at arbitrarily small entropy production, yet at the expense of diverging activity. For a fixed activity, we find that the dynamics that minimizes the entropy production is driven by conservative forces. The value of the minimum entropy production is expressed in terms of the graph-distance based Wasserstein distance between the initial and final configuration. This yields a new kind of speed limit relating dissipation, the average number of transitions and the Wasserstein distance. It also allows us to formulate the optimal transport problem on a graph via continuous-time interpolating dynamics, in complete analogy to the continuous space setting. We demonstrate our findings for simple state networks, a time-dependent pump and for spin flips in the Ising model.

Dissipation of moving vortices in thin films

Moving vortices in thin superconducting films are considered within the time-dependent London description. The dissipation due to out-of-core normal excitations for two vortices moving together turns out to have a minimum for the separation vector $\bm a$ parallel to the velocity and equal to $a_m \approx 2.2\, \Lambda$, where $\Lambda $ is the Pearl length. The minimum entropy production suggests that moving vortices should have a tendency to form chains along the velocity with a period of the order $a_m$.

Numerical simulation of thermo-magnetic convection and entropy production in a ferrofluid filled square chamber with effects of heat generating solid body

Thermo-magnetic convection and entropy production are the most widely used subjects of study in the field of an effective design tools for cooling electronic devices. The present work focuses on numerical simulation of thermo-magnetic convection cooling of the heat-generating solid block placed in a magnetite suspended nanoliquid filled chamber. The surfaces of the horizontal borders of the chamber are thermally insulated whilst the vertical borders are cooled at a constant temperature. The finite volume technique with a simple algorithm on a uniform staggered grid is employed to transform the governing non-linear PDE into a set of discretized equations. The liquid motion, thermal transmission, and entropy production are discussed for various pertinent parameters such as solid volume fractions of the nano-additive (φ=0.01−0.04), aspect ratio of a heat-generating solid body (As=0.25−4), thermal conductivity ratio of the heat generating body (0.1≤k*≤5.0), Hartmann number (Ha=0−50) and irreversibility ratio (Ω=0.001−0.1). Isolines of temperature, stream function, normalized entropy along with profiles of mean Nusselt number and mean entropy production outcomes are demonstrated graphically. The results showed that reduction in aspect ratio increases the cooling efficiency due to the hindrance-free effect and produces a high heat transfer rate. Minimum entropy production occurs at low thermal conductivity ratio (k*=0.1). The thermal performance criterion also justifies that the least aspect ratio manifests better thermal performance.

Are peatlands in different states with respect to their thermodynamic behaviour? A simple test of peatland energy and entropy budgets

AbstractWhilst all ecosystems must obey the second law of thermodynamics, these physical bounds and controls on ecosystem evolution and development are largely ignored across the ecohydrological literature. To unravel the importance of these underlying restraints on ecosystem form and function, and their power to inform our scientific understanding, we have calculated the entropy budget of a range of peat ecosystems. We hypothesize that less disturbed peatlands are ‘near equilibrium’ with respect to the second law of thermodynamics and thus respond to change by minimizing entropy production. This ‘near equilibrium’ state is best achieved by limiting evaporative losses. Alternatively, peatlands ‘far‐from‐equilibrium’ respond to a change in energy inputs by maximizing entropy production which is best achieved by increasing evapotranspiration. To test these alternatives this study examined the energy balance time series from seven peatlands across a disturbance gradient. We estimate the entropy budgets for each and determine how a change in net radiation (ΔRn) was transferred to a change in latent heat flux (ΔλE). The study showed that: (i) The transfer of net radiation to latent heat differed significantly between peatlands. One group transferred up to 64% of the change in net radiation to a change in latent heat flux, while the second transferred as little as 27%. (ii) Sites that transferred the most energy to latent heat flux were those that produced the greatest entropy. The study shows that an ecosystem could be ‘near equilibrium’ rather than ‘far from equilibrium’.

A novel comparative case study of entropy generation for natural convection flow of proportional-Caputo hybrid and Atangana baleanu fractional derivative

This article focused on the comparative study of entropy generation for natural convection flow of the newly proportional Caputo hybrid and Atangana baleanu fractional derivative. The governing equation is formed as the set of partial differential equations with the physical boundary conditions. The report of entropy generation is investigated for the first time for proportional–Caputo hybrid model and comparison are sorts out with generalized Atangana baleanu fractional derivative. The Bejan number is also compared for the mention fractional derivatives. Graphs show the impact of various factors on the minimization and maximizing of entropy production. The newly proportional Caputo hybrid operator has a good memory effect rather than Atangana baleanu fractional operator.

Dependence of integrated, instantaneous, and fluctuating entropy production on the initial state in quantum and classical processes.

We consider the additional entropy production (EP) incurred by a fixed quantum or classical process on some initial state ρ, above the minimum EP incurred by the same process on any initial state. We show that this additional EP, which we term the "mismatch cost of ρ," has a universal information-theoretic form: it is given by the contraction of the relative entropy between ρ and the least-dissipative initial state φ over time. We derive versions of this result for integrated EP incurred over the course of a process, for trajectory-level fluctuating EP, and for instantaneous EP rate. We also show that mismatch cost for fluctuating EP obeys an integral fluctuation theorem. Our results demonstrate a fundamental relationship between thermodynamic irreversibility (generation of EP) and logical irreversibility (inability to know the initial state corresponding to a given final state). We use this relationship to derive quantitative bounds on the thermodynamics of quantum error correction and to propose a thermodynamically operationalized measure of the logical irreversibility of a quantum channel. Our results hold for both finite- and infinite-dimensional systems, and generalize beyond EP to many other thermodynamic costs, including nonadiabatic EP, free-energy loss, and entropy gain.

Numerical investigation of the nozzle expansion state and its effect on the performance of the steam ejector based on ideal gas model

Many research works have generally divided the back pressure range of steam ejectors into critical, subcritical and malfunction modes based on the change of the entrainment ratio. In this study, we innovatively define and compare the abnormal and normal modes of the over-expanded, fully expanded and under-expanded states for a steam ejector using the CFD method and find that the steam ejector can maintain almost the same the secondary fluid mass flow rate under the normal mode of different expanded states. A comparison of different nozzle expansion states is also carried out. The results demonstrate that huge flow separation zones occur in the mixing chamber and diffuser in the under-expanded state, causing a drop in the secondary fluid mass flow rate compared with other expanded states. In addition, the irreversibility analysis illustrates that the steam ejector could minimize entropy production under the over-expansion state to obtain the optimal entrainment rate. More importantly, this paper provides a theoretical reference for maximizing the entrainment ratio or the secondary fluid mass flow rate from the perspective of the nozzle expansion state.

Dependence of Resistance and Number of Tapes on the Coupling AC Loss of Soldered REBCO Stacks

HTS stack has high current carrying capacity which is widely used in motors or generators. Usually, the HTS tapes are stacked and soldered together at ends. Although the HTS tapes are insulated and have low loss, the soldering parts are conventional conductors with resistance. When the HTS stack is subject to a parallel ac magnetic field, the coupling currents are induced because of the soldered parts which would form current loops. And then, the coupling currents would cause coupling loss or been called resistance loss. The loss is not only related to the applied field but also depends on the number of tapes and resistance value. The minimum electromagnetic entropy production method is used to study the dependence of resistance and number of tapes on the magnetization loss systematically. A HTS stack with realistic resistance was prepared and measured to be verified the calculation. The results show that the superconductor loss increases at the beginning but then decreases later when more tapes are stacked. However, the resistance loss increases almost linearly. The resistance loss and the superconductor loss also depend on the resistance value. When the resistance is small, although there are coupling currents pass through the ending parts, the resistance value is so small that the resistance loss is very difficult to be observed. And the resistance loss would increase with the resistance linearly and the superconductor loss almost keeps constant. With the resistance increasing, there is a peak in the resistance loss and the superconductor loss drops dramatically. Later, the resistance loss decreases with the resistance and the superconductor loss keeps constant again, because the resistance is so large that no coupling current can pass through the soldering parts so that there is almost no resistance at all.

Variational formulation of non-equilibrium void fraction

A general variational formulation of the dissipative two-phase flows based on the extremization of the entropy production is developed. The entropy generation rate is written outside phase equilibrium by introducing interfacial contributions due to surface tension as well as heat and mass transfer between the two phases. Prigogine's theorem of minimum entropy production is used to estimate the steady state void fraction of the two-phase flow. The corresponding flow representation is investigated out of phase equilibrium for an annular flow, experiencing friction, surface tension effects, and interphase heat and mass transfer, within a diabatic channel. It is demonstrated that the present formulation generalises previous theories by capturing the effect of mass and heat fluxes variations, and that the widely accepted expression from Zivi represents a particular case obtained under certain simplifying assumptions. Finally, a first validation of the developed formulation of two-phase void fraction is presented for different flow conditions, heat flux from the external environment, and thermophysical properties of the refrigerant with reference to data obtained from a dedicated experimental apparatus adopting a capacitance sensor and from previous literature.