Energetic Self-Optimization Induced by Stability in Low-Dissipation Heat Engines

Energy conversion theorems for some linear steady states

One of the main issues that real energy converters present, when they produce effective work, is the inevitable entropy production. Within the context of nonequilibrium thermodynamics, entropy production tends to energetically degrade human-made or living systems. On the other hand, it is not useful to think about designing an energy converter that works in the so-called minimum entropy production regime since the effective power output and efficiency are zero. In this paper we establish some energy conversion theorems similar to Prigogine's theorem with constrained forces. The purpose of these theorems is to reveal trade-offs between design and the so-called operation modes for (2×2)-linear isothermal energy converters. The objective functions that give rise to those thermodynamic constraints show stability. A two-mesh electric circuit was built as an example to demonstrate the theorems' validity. Likewise, we reveal a type of energetic hierarchy for power output, efficiency, and dissipation function when the circuit is tuned to any of the operating regimes studied here. These are maximum power output (MPO), maximum efficient power (MPη), maximum omega function (MΩ), maximum ecological function (MEF), maximum efficiency (Mη), and minimum dissipation function (mdf).

Performance of Quantum Heat Engines Enhanced by Adiabatic Deformation of Trapping Potential

We present a quantum Otto engine model alternatively driven by a hot and a cold heat reservoir and consisting of two isochoric and two adiabatic strokes, where the adiabatic expansion or compression is realized by adiabatically changing the shape of the potential. Here, we show that such an adiabatic deformation may alter operation mode and enhance machine performance by increasing output work and efficiency, even with the advantage of decreasing work fluctuations. If the heat engine in the sudden limit operates under maximal power by optimizing the control parameter, the efficiency shows certain universal behavior, η*=ηC/2+ηC2/8+O(ηC3), where ηC=1-βhr/βcr is the Carnot efficiency, with βhr(βcr) being the inverse temperature of the hot (cold) reservoir. However, such efficiency under maximal power can be produced by our machine model in the regimes where the machine without adiabatic deformation can only operate as a heater or a refrigerator.

Low-dissipation optimization of the prefrontal cortex in the -12° head-down tilt position: A functional near-infrared spectroscopy study

Introduction

Our present study set out to investigate the instant state of the prefrontal cortex (PFC) in healthy subjects before and after placement in the -12°head-down tilt (HDT) position in order to explore the mechanism behind the low-dissipation optimization state of the PFC.

Methods

40 young, right-handed healthy subjects (male: female = 20: 20) were enrolled in this study. Three resting state positions, 0°initial position, -12°HDT position, and 0°rest position were sequentially tested, each for 10 minutes. A continuous-wave functional near-infrared spectroscopy (fNIRS) instrument was used to assess the resting state hemodynamic data of the PFC. After preprocessing the hemodynamics data, we evaluated changes in resting-state functional connectivity (rsFC) level and beta values of PFC. The subjective visual analogue scale (VAS) was applied before and after the experiment. The presence of sleep changes or adverse reactions were also recorded.

Results

Pairwise comparisons of the concentrations of oxyhemoglobin (HbO), deoxyhemoglobin (HbR), and hemoglobin (HbT) revealed significant differences in the aforementioned positions. Specifically, the average rsFC of PFC showed a gradual increase throughout the whole process. In addition, based on graph theory, the topological properties of brain network, such as small-world network and nodal degree centrality were analyzed. The results show that global efficiency and small-world sigma (σ) value were differences between 0°initial and 0°rest.

Discussion

In this study, placement in the -12°HDT had a significant effect on PFC function, mainly manifested as self-inhibition, decreased concentration of HbO in the PFC, and improved rsFC, which may provide ideas to the understanding and explanation of neurological diseases.

Microscopic theory of the Curzon-Ahlborn heat engine based on a Brownian particle

The Curzon-Ahlborn (CA) efficiency, as the efficiency at the maximum power (EMP) of the endoreversible Carnot engine, has significant impact on finite-time thermodynamics. However, the CA engine is based on many assumptions. In the past few decades, although a lot of efforts have been made, a microscopic theory of the CA engine is still lacking. By adopting the method of the stochastic differential equation of energy, we formulate a microscopic theory of the CA engine realized with a highly underdamped Brownian particle in a class of nonharmonic potentials. This theory gives microscopic interpretation of all assumptions made by Curzon and Ahlborn. In other words, we find a microscopic counterpart of the CA engine in stochastic thermodynamics. Also, based on this theory, we derive the explicit expression of the protocol associated with the maximum power for any given efficiency, and we obtain analytical results of the power and the efficiency statistics for the Brownian CA engine. Our research brings new perspectives to experimental studies of finite-time microscopic heat engines featured with fluctuations.

Maximum efficiency of low-dissipation heat pumps at given heating load

We derive an analytical expression for maximum efficiency at fixed power of heat pumps operating along a finite-time reverse Carnot cycle under the low-dissipation assumption. The result is cumbersome, but it implies simple formulas for tight upper and lower bounds on the maximum efficiency and various analytically tractable approximations. In general, our results qualitatively agree with those obtained earlier for endoreversible heat pumps. In fact, we identify a special parameter regime when the performance of the low-dissipation and endoreversible devices is the same. At maximum power, heat pumps operate as work to heat converters with efficiency 1. Expressions for maximum efficiency at given power can be helpful in the identification of more practical operation regimes.

Success versus failure: Efficient heat devices in thermodynamics

Classical equilibrium thermodynamics provides, in a general way, upper Carnot bounds for the performance of energy converters. Nevertheless, to suggest lower bounds is a much more subtle issue, especially when they are related to a definition of convenience. Here, this issue is investigated in a unified way for heat engines, refrigerators, and heat pumps. First, irreversibilities are weighted in the context of heat reservoir stability for irreversible engines by using the thermodynamic distance between minimum energy and maximum entropy steady states. Some stability coefficients can be related to a majorization process and the obtention of Pareto fronts, linking stability and optimization by means of efficiency and entropy due to correlations between system and reservoirs. Second, these findings are interpreted in a very simple context. A region where the heat device is efficient is defined in a general scheme and, below this zone, the heat device is inefficient in the sense that irreversibilities somehow dominate its behavior. These findings allow for a clearer understanding of the role played by some well-known figures of merit in the scope of finite-time and -size optimization. Comparison with experimental results is provided.

Performance Analysis and Four-Objective Optimization of an Irreversible Rectangular Cycle

Based on the established model of the irreversible rectangular cycle in the previous literature, in this paper, finite time thermodynamics theory is applied to analyze the performance characteristics of an irreversible rectangular cycle by firstly taking power density and effective power as the objective functions. Then, four performance indicators of the cycle, that is, the thermal efficiency, dimensionless power output, dimensionless effective power, and dimensionless power density, are optimized with the cycle expansion ratio as the optimization variable by applying the nondominated sorting genetic algorithm II (NSGA-II) and considering four-objective, three-objective, and two-objective optimization combinations. Finally, optimal results are selected through three decision-making methods. The results show that although the efficiency of the irreversible rectangular cycle under the maximum power density point is less than that at the maximum power output point, the cycle under the maximum power density point can acquire a smaller size parameter. The efficiency at the maximum effective power point is always larger than that at the maximum power output point. When multi-objective optimization is performed on dimensionless power output, dimensionless effective power, and dimensionless power density, the deviation index obtained from the technique for order preference by similarity to an ideal solution (TOPSIS) decision-making method is the smallest value, which means the result is the best.

Maximum efficiency of absorption refrigerators at arbitrary cooling power

We consider absorption refrigerators consisting of simultaneously operating Carnot-type heat engine and refrigerator. Their maximum efficiency at given power (MEGP) is given by the product of MEGPs for the internal engine and refrigerator. The only subtlety of the derivation lies in the fact that the maximum cooling power of the absorption refrigerator is not limited just by the maximum power of the internal refrigerator, but, due to the first law, also by that of the internal engine. As a specific example, we consider the simultaneous absorption refrigerators composed of low-dissipation (LD) heat engines and refrigerators, for which the expressions for MEGPs are known. The derived expression for maximum efficiency implies bounds on the MEGP of LD absorption refrigerators. It also implies that a slight decrease in power of the absorption refrigerator from its maximum value results in a large nonlinear increase in efficiency, observed in heat engines, whenever the ratio of maximum powers of the internal engine and the refrigerator does not diverge. Otherwise, the increase in efficiency is linear as observed in LD refrigerators. Thus, in all practical situations, the efficiency of LD absorption refrigerators significantly increases when their cooling power is slightly decreased from its maximum.

Optimization, Stability, and Entropy in Endoreversible Heat Engines

The stability of endoreversible heat engines has been extensively studied in the literature. In this paper, an alternative dynamic equations system was obtained by using restitution forces that bring the system back to the stationary state. The departing point is the assumption that the system has a stationary fixed point, along with a Taylor expansion in the first order of the input/output heat fluxes, without further specifications regarding the properties of the working fluid or the heat device specifications. Specific cases of the Newton and the phenomenological heat transfer laws in a Carnot-like heat engine model were analyzed. It was shown that the evolution of the trajectories toward the stationary state have relevant consequences on the performance of the system. A major role was played by the symmetries/asymmetries of the conductance ratio σhc of the heat transfer law associated with the input/output heat exchanges. Accordingly, three main behaviors were observed: (1) For small σhc values, the thermodynamic trajectories evolved near the endoreversible limit, improving the efficiency and power output values with a decrease in entropy generation; (2) for large σhc values, the thermodynamic trajectories evolved either near the Pareto front or near the endoreversible limit, and in both cases, they improved the efficiency and power values with a decrease in entropy generation; (3) for the symmetric case (σhc=1), the trajectories evolved either with increasing entropy generation tending toward the Pareto front or with a decrease in entropy generation tending toward the endoreversible limit. Moreover, it was shown that the total entropy generation can define a time scale for both the operation cycle time and the relaxation characteristic time.

Thermodynamic optimization subsumed in stability phenomena

In the present paper the possibility of an energetic self-optimization as a consequence of thermodynamic stability is addressed. This feature is analyzed in a low dissipation refrigerator working in an optimized trade-off regime (the so-called Omega function). The relaxation after a perturbation around the stable point indicates that stability is linked to trajectories in which the thermodynamic performance is improved. Furthermore, a limited control over the system is analyzed through consecutive external random perturbations. The statistics over many cycles corroborates the preference for a better thermodynamic performance. Endoreversible and irreversible behaviors play a relevant role in the relaxation trajectories (as well as in the statistical performance of many cycles experiencing random perturbations). A multi-objective optimization reveals that the well-known endoreversible limit works as an attractor of the system evolution coinciding with the Pareto front, which represents the best energetic compromise among efficiency, entropy generation, cooling power, input power and the Omega function. Meanwhile, near the stable state, performance and stability are dominated by an irreversible behavior.

Maximum efficiency of low-dissipation refrigerators at arbitrary cooling power

We analytically derive maximum efficiency at given cooling power for Carnot-type low-dissipation refrigerators. The corresponding optimal cycle duration depends on a single parameter, which is a specific combination of irreversibility parameters and bath temperatures. For a slight decrease in power with respect to its maximum value, the maximum efficiency exhibits an infinitely fast nonlinear increase, which is standard in heat engines, only for a limited range of parameters. Otherwise, it increases only linearly with the slope given by ratio of irreversibility parameters. This behavior can be traced to the fact that maximum power is attained for vanishing duration of the hot isotherm. Due to the lengthiness of the full solution for the maximum efficiency, we discuss and demonstrate these results using simple approximations valid for parameters yielding the two different qualitative behaviors. We also discuss relation of our findings to those obtained for minimally nonlinear irreversible refrigerators.