Minimum Entropy Production Rate Research Articles

Entropy analyses of electronic devices with different energy selective electron tunnels

Based on nanoelectronic devices that can act as power generators or refrigerators, the relations between the entropy production rate and the thermal efficiency or coefficient of performance are obtained for two types of electron filters. It is found that the decrease of the entropy production rate does not always guarantee the increase of the thermal efficiency or coefficient of performance, indicating that the state of the minimum entropy production rate does not correspond to that of the maximum thermal efficiency or coefficient of performance in these electronic devices. It implies the fact that different from the thermal efficiency or coefficient of performance, the entropy production rate is not a good objective function for optimizing the performance of electronic devices. However, entropy analyses will be helpful to deeply understanding the thermodynamic properties of electronic devices. These results obtained here will provide a feasible scheme to further optimize and improve the performances of electronic devices.

Thermo-ecological analysis and optimization of a three-heat-reservoir absorption heat pump with two internal irreversibilities and external irreversibility

The investigations carried out in this work concern the optimization and the thermodynamic analysis of an absorption heat pump with multi-irreversibilities and provided with three-heat-reservoir mainly using the thermo-ecological criterion as objective function. The thermodynamic analysis of the first and second laws of thermodynamics and the linear law of heat-transfer allowed us to evaluate and optimize the objective functions of performance such as: the specific heating load, the coefficient of performance, the specific entropy generation rate, the ecological coefficient of performance and the heat-transfer areas of the various components. These allowed us to study the variations of these criteria according to the design parameters and the temperatures of the working fluid in the components. From this study, it follows that the optimal system implies a maximum thermo-ecological coefficient, a minimum entropy production rate corresponding to a certain value of the specific heating load, while maintaining a system which limits the losses between the condenser and the evaporator. Moreover, the consideration of the two internal irreversibilities, the external irreversibility and the losses of the heat resistances is very close to a real absorption heat pump and allows a more precise and objective study rather than in the optimization and the design of an absorption system like an endoreversible system.

Non-Equilibrium Thermodynamics and Stochastic Dynamics of a Bistable Catalytic Surface Reaction.

Catalytic surface reaction networks exhibit nonlinear dissipative phenomena, such as bistability. Macroscopic rate law descriptions predict that the reaction system resides on one of the two steady-state branches of the bistable region for an indefinite period of time. However, the smaller the catalytic surface, the greater the influence of coverage fluctuations, given that their amplitude normally scales as the square root of the system size. Thus, one can observe fluctuation-induced transitions between the steady-states. In this work, a model for the bistable catalytic CO oxidation on small surfaces is studied. After a brief introduction of the average stochastic modelling framework and its corresponding deterministic limit, we discuss the non-equilibrium conditions necessary for bistability. The entropy production rate, an important thermodynamic quantity measuring dissipation in a system, is compared across the two approaches. We conclude that, in our catalytic model, the most favorable non-equilibrium steady state is not necessary the state with the maximum or minimum entropy production rate.

The cancer Warburg effect may be a testable example of the minimum entropy production rate principle

Cancer cells consume more glucose by glycolytic fermentation to lactate than by respiration, a characteristic known as the Warburg effect. In contrast with the 36 moles of ATP produced by respiration, fermentation produces two moles of ATP per mole of glucose consumed, which poses a puzzle with regard to the function of the Warburg effect. The production of free energy (ΔG), enthalpy (ΔH), and entropy (ΔS) per mole linearly varies with the fraction (x) of glucose consumed by fermentation that is frequently estimated around 0.9. Hence, calculation shows that, in respect to pure respiration, the predominant fermentative metabolism decreases around 10% the production of entropy per mole of glucose consumed in cancer cells. We hypothesize that increased fermentation could allow cancer cells to accomplish the Prigogine theorem of the trend to minimize the rate of production of entropy. According to the theorem, open cellular systems near the steady state could evolve to minimize the rates of entropy production that may be reached by modified replicating cells producing entropy at a low rate. Remarkably, at CO2 concentrations above 930 ppm, glucose respiration produces less entropy than fermentation, which suggests experimental tests to validate the hypothesis of minimization of the rate of entropy production through the Warburg effect.

The equivalence of minimum entropy production and maximum thermal efficiency in endoreversible heat engines

The objective of this study is to investigate the thermal efficiency and power production of typical models of endoreversible heat engines at the regime of minimum entropy generation rate. The study considers the Curzon-Ahlborn engine, the Novikov’s engine, and the Carnot vapor cycle. The operational regimes at maximum thermal efficiency, maximum power output and minimum entropy production rate are compared for each of these engines. The results reveal that in an endoreversible heat engine, a reduction in entropy production corresponds to an increase in thermal efficiency. The three criteria of minimum entropy production, the maximum thermal efficiency, and the maximum power may become equivalent at the condition of fixed heat input.

Derivation and verification of minimum energy dissipation rate principle of fluid based on minimum entropy production rate principle

Based on non-equilibrium thermodynamics theory, minimum energy dissipation rate principle can be derived from minimum entropy production rate principle. Minimum entropy production rate principle is equivalent to minimum energy dissipation rate principle. In order to verify the fluid motion following minimum energy dissipation rate principle, RNG k−ε turbulence model and GMO model of Flow 3D were applied to simulate fluid motion in a straight rectangular flume. The results show that fluid motion satisfies the minimum energy dissipation rate principle. The validity of minimum energy dissipation rate of alluvial rivers has been tested with field data. When a river system is at a relative equilibrium state, the value of its energy dissipation rate is at minimum. The minimum value depends on the constraints applied to the river system. However, due to the dynamic nature of a river, the minimum value may vary with respective to time and location. Minimum stream power and minimum unit stream power principles are special and simplified versions of the more general minimum energy dissipation rate principle.

Use and validity of principles of extremum of entropy production in the study of complex systems

It is shown how both the principles of extremum of entropy production, which are often used in the study of complex systems, follow from the maximization of overall system conductivities, under appropriate constraints. In this way, the maximum rate of entropy production (MEP) occurs when all the forces in the system are kept constant. On the other hand, the minimum rate of entropy production (mEP) occurs when all the currents that cross the system are kept constant. A brief discussion on the validity of the application of the mEP and MEP principles in several cases, and in particular to the Earth’s climate is also presented.

From the Viewpoint of Water-Sediment Characters to Approach the General Criteria for Waterway Regulating with Complex Shoals

Compared with each other of existed schemes and effects of the waterway regulating with complex shoals, from the viewpoint of water-sediment interacting evolutional properties and their effects on complex shoals of waterway, the results show that, the evolutional processes of channel morphology observe the principles of maximum entropy in equilibrium state and minimum entropy production rate in non-equilibrium state, in energy words, it is the minimum energy dissipation rate. The vortex moving dominates the sediment transport. From the practical engineering viewpoint, the general criteria for waterway regulating with complex shoals were investigated, the results may be valuable to regulating study of the mountain rivers.

Irreversibility in biophysical and biochemical engineering

The thermodynamic analysis of open systems is fundamental in engineering. For the open systems at their steady state, two apparently opposed principles for the rate of entropy production have been used: the minimum entropy production rate derived by Prigogine, used in the description of various processes in physics, chemistry and biology, and the maximum entropy production, used in many other cases and now considered more general. Both principles involve an extreme value of the rate of entropy production in an open system at the steady state under non-equilibrium conditions. In this paper, a link between these two approaches is developed and their synthesis with the constructal law is proposed. An application to ATP synthesis in anaerobic fermentation for biogas production is presented.

Finite time thermodynamic optimization for heat-driven binary separation processes

The performance of heat-driven binary separation processes with linear phenomenological heat transfer law (q ∞ Δ(T −1) is optimized by using finite time thermodynamics. Two performance indexes, the dimensionless minimum average entropy production rate and dimensionless minimum average heat consumption of the heat-driven binary separation processes, are taken as optimization objectives, respectively. The separation processes are viewed as heat engines which work between high- and low-temperature reservoirs and produce enthalpy and energy flows out of the system. The temperatures of the heat reservoirs are assumed to be time- and space-variables. The convex optimization problem is solved using numerical method, and the average optimal control problem is solved using Lagrangian function. The major influence factors on the performance of the separation process, such as the properties of different materials and various separation requirements for the separation process, are represented by dimensionless entropy production rate coefficient and dimensionless enthalpy flow rate coefficient. The dimensionless minimum average entropy production rate and dimensionless minimum average heat consumption of the heat-driven binary separation processes are obtained, respectively.

Modeling Electric Discharges with Entropy Production Rate Principles

Under which circumstances are variational principles based on entropy production rate useful tools for modeling steady states of electric (gas) discharge systems far from equilibrium? It is first shown how various different approaches, as Steenbeck’s minimum voltage and Prigogine’s minimum entropy production rate principles are related to the maximum entropy production rate principle (MEPP). Secondly, three typical examples are discussed, which provide a certain insight in the structure of the models that are candidates for MEPP application. It is then thirdly argued that MEPP, although not being an exact physical law, may provide reasonable model parameter estimates, provided the constraints contain the relevant (nonlinear) physical effects and the parameters to be determined are related to disregarded weak constraints that affect mainly global entropy production. Finally, it is additionally conjectured that a further reason for the success of MEPP in certain far from equilibrium systems might be based on a hidden linearity of the underlying kinetic equation(s).

The minimum heat consumption for heat-driven binary separation processes with linear phenomenological heat transfer law

The optimal performance of heat-driven binary separation processes with linear phenomenological heat transfer law (q∝Δ(T −1)) is analyzed by taking the processes as heat engines which work between high- and low-temperature reservoirs and produce enthalpy and energy flows out of the system, and the temperatures of the heat reservoirs are assumed to be time- and space-variables. A numerical method is employed to solve convex optimization problem and Lagrangian function is employed to solve the average optimal control problem. The dimensionless entropy production rate coefficient and dimensionless enthalpy flow rate coefficient are adopted to indicate the major influence factors on the performance of the separation process, such as the properties of different materials and various separation requirements for the separation process. The dimensionless minimum average entropy production rate and dimensionless minimum average heat consumption of the heat-driven binary separation processes are obtained. The obtained results are compared with those obtained with the Newtonian heat transfer law (q∝Δ(T)).

Thermodynamic analysis of stream flow hydrodynamics

The equation for entropy generation is derived directly from the conservation equations for one-dimensional (1D) channel flow. Mass, momentum, and energy equations are averaged from their microscale forms to the 1D forms used in channel modeling while allowing for channel curvature. The equations of classical irreversible thermodynamics are also averaged so that macroscale energy and entropy are consistently and uniquely related. These averaged equations serve as constraints on an averaged entropy inequality so that the dissipative processes are quantified and can be analyzed for cases where the rate of entropy production is minimized. Specifically, the case of uniform flow in a prismatic channel is presented; and the entropy production rate is obtained. Also, the case of gradually varied flow in a wide rectangular channel is presented and analyzed for conditions of a minimum rate of entropy production. For both these cases, the impact of a nonuniform velocity profile over the flow cross section is accounted for.

Thermodynamics of surface degradation, self-organization and self-healing for biomimetic surfaces

Friction is a dissipative irreversible process; therefore, entropy is produced during frictional contact. The rate of entropy production can serve as a measure of degradation (e.g. wear). However, in many cases friction leads to self-organization at the surface. This is because the excess entropy is either driven away from the surface, or it is released at the nanoscale, while the mesoscale entropy decreases. As a result, the orderliness at the surface grows. Self-organization leads to surface secondary structures either due to the mutual adjustment of the contacting surfaces (e.g. by wear) or due to the formation of regular deformation patterns, such as friction-induced slip waves caused by dynamic instabilities. The effect has practical applications, since self-organization is usually beneficial because it leads to friction and wear reduction (minimum entropy production rate at the self-organized state). Self-organization is common in biological systems, including self-healing and self-cleaning surfaces. Therefore, designing a successful biomimetic surface requires an understanding of the thermodynamics of frictional self-organization. We suggest a multiscale decomposition of entropy and formulate a thermodynamic framework for irreversible degradation and for self-organization during friction. The criteria for self-organization due to dynamic instabilities are discussed, as well as the principles of biomimetic self-cleaning, self-lubricating and self-repairing surfaces by encapsulation and micro/nanopatterning.

Minimum dissipative relaxed states applied to laboratory and space plasmas

AbstractThe usual theory of plasma relaxation, based on the selective decay of magnetic energy over the (global) magnetic helicity, predicts a force-free state for a plasma. Such a force-free state is inadequate to describe most realistic plasma systems occurring in laboratory and space plasmas as it produces a zero pressure gradient and cannot couple magnetic fields with flow. A different theory of relaxation has been proposed by many authors, based on a well-known principle of irreversible thermodynamics, the principle of minimum entropy production rate which is equivalent to the minimum dissipation rate of energy. We demonstrate the applicability of minimum dissipative relaxed states to various self-organized systems of magnetically confined plasma in the laboratory and in the astrophysical context. Such relaxed states are shown to produce a number of basic characteristics of laboratory plasma confinement systems and solar arcade structure.

Optimal performance of an endoreversible chemical pump with diffusive mass transfer law

The performance of an isothermal endoreversible two-reservoir chemical pump, in which the mass transfer obeys diffusive law, is analysed and optimised in this paper. The relation between the rate of energy pumping and the coefficient of performance of the isothermal chemical pump is derived by using finite-time thermodynamics. Moreover, the relation between the minimum power input and the coefficient of performance, and the relation between the minimum entropy production rate and the rate of energy pumping are obtained. The results obtained herein can provide some new theoretical guidelines for the optimal design of a class of apparatus such as mass exchangers, as well as electrochemical, photochemical, solid-state devices, and the fuel pumps for solar-energy conversion systems.

Powering Mercury's dynamo

The presence of the global magnetic field of Mercury has implications for the interior structure of the planet and its thermal evolution. We use a thermal evolution model to explore the conditions under which excess entropy is available to drive a convective dynamo. The current state of the core is strongly affected by its sulfur concentration and the viscosity of the overlying mantle. A present‐day dynamo is difficult to achieve. The minimum rate of entropy production required to drive a dynamo is attained in only the most optimistic models, and requires present‐day mantle convection. An additional entropy source such as the addition of a radiogenic heat source in the core increases the probability of a present‐day dynamo. Given the uncertainty, more specific characterization of the planet's interior and magnetic field is required to alleviate ambiguities in the original Mariner 10 observations.

Statistical mechanical theory for steady state systems. VI. Variational principles

Several variational principles that have been proposed for nonequilibrium systems are analyzed. These include the principle of minimum rate of entropy production due to Prigogine [Introduction to Thermodynamics of Irreversible Processes (Interscience, New York, 1967)], the principle of maximum rate of entropy production, which is common on the internet and in the natural sciences, two principles of minimum dissipation due to Onsager [Phys. Rev. 37, 405 (1931)] and to Onsager and Machlup [Phys. Rev. 91, 1505 (1953)], and the principle of maximum second entropy due to Attard [J. Chem.. Phys. 122, 154101 (2005); Phys. Chem. Chem. Phys. 8, 3585 (2006)]. The approaches of Onsager and Attard are argued to be the only viable theories. These two are related, although their physical interpretation and mathematical approximations differ. A numerical comparison with computer simulation results indicates that Attard's expression is the only accurate theory. The implications for the Langevin and other stochastic differential equations are discussed.

Application of the maximum entropy production principle to electrical systems

For a simple class of electrical systems, the principle of the maximum entropy production rate (MaxEP) is discussed. First, we compare the MaxEP principle and the principle of the minimum entropy production rate and illustrate the superiority of the MaxEP principle for the example of two parallel constant resistors. Secondly, we show that the Steenbeck principle for the electric arc as well as the ohmic contact behaviour of space-charge limited conductors follow from the MaxEP principle. In line with work by Dewar, the investigations seem to suggest that the MaxEP principle can also be applied to systems far from equilibrium, provided appropriate information is available that enters the constraints of the optimization problem. Finally, we apply the MaxEP principle to a mesoscopic system and show that the universal conductance quantum, e2/h, of a one-dimensional ballistic conductor can be estimated.

Extremum principles for irreversible processes

Hamilton’s extremum principle is a powerful mathematical tool in classical mechanics. Onsager’s extremum principle may play a similar role in irreversible thermodynamics and may also become a valuable tool. His principle may formally be regarded as a principle of maximum rate of entropy production but does not have a clear physical interpretation. Prigogine’s principle of minimum rate of entropy production has a physical interpretation when it applies, but is not strictly valid except for a very special case.