一维晶格中费曼棘齿-棘爪热机

研究了一维晶格中费曼棘齿-棘爪热机模型. 用粒子的概率主方程来描述粒子在晶格中的动力学特性, 推导出热流、 功率和效率的表达式. 通过数值计算分析势垒高度、 外力和温比对热流以及热机功率和效率的影响. 研究表明: 在粒子稳态概率流为零时, 存在非零的热流从高温库流入低温库, 类似于经典不可逆卡诺模型中的热漏; 热漏的存在使得热机的效率远远小于卡诺效率, 功率与效率之间为闭合的关系曲线, 热机为不可逆热机; 对热机性能参数进行优化, 可以使热机工作在最优性能状态下.     

Stochastic dynamics,efficiency and sustainable power production

In the framework of stochastic thermodynamics, we give a precise expression of power dissipation in a heat engine, and study the relation between entropy and power dissipation. Using these relations, we propose a reasonable and general definition of efficiency for thermal engines in a non-equilibrium stationary state. This definition, different from Carnot efficiency, seems appropriate to the concerns of sustainable development. We show that non-zero dissipation is necessary for producing non-vanishing power. Furthermore, close to equilibrium and even in much broader situations, when power production is maximum with respect to relevant variables the power dissipation is at less equal to the power delivered to a mechanical, external system, and the corresponding “sustainable efficiency” is at most ?. From this result, we deduce a new upper bound for Carnot efficiency at maximum power. It is compared to similar, but different upper bounds obtained previously by other authors.     

Performance characteristics of an irreversible thermally driven Brownian microscopic heat engine

Brownian particles moving in a spatially asymmetric but periodic potential (ratchet), with an external load force and connected to an alternating hot and cold reservoir, are modeled as a microscopic heat engine, referred to as the Brownian heat engine. The heat flow via both the potential energy and the kinetic energy of the particles are considered simultaneously. The forward and backward particle currents are determined using an Arrhenius' factor. Expressions for the power output and efficiency are derived analytically. The maximum power output and efficiency are calculated. It is expounded that the Brownian heat engine is always irreversible and its efficiency cannot approach the efficiency η_C of the Carnot heat engine even in quasistatic limit. The influence of the main parameters such as the load, the barrier height of the potential, the asymmetry of the potential and the temperature ratio of the heat reservoirs on the performance of the Brownian heat engine is discussed in detail. It is found that the Brownian heat engines may be controlled to operate in different regions through variation of some parameters.     

Performance characteristics of low-dissipative generalized Carnot cycles with external leakage losses

Under the assumption of low-dissipation, a unified model of generalized Carnot cycles with external leakage losses is established. Analytical expressions for the power output and efficiency are derived. The general performance characteristics between the power output and the efficiency are revealed. The maximum power output and efficiency are calculated. The lower and upper bounds of the efficiency at the maximum power output are determined. The results obtained here are universal and can be directly used to reveal the performance characteristics of different Carnot cycles, such as Carnot heat engines, Carnot-like heat engines, flux flow engines, gravitational engines, chemical engines, two-level quantum engines,etc.     

Efficiency bounds for nonequilibrium heat engines

We analyze the efficiency of thermal engines (either quantum or classical) working with a single heat reservoir like an atmosphere. The engine first gets an energy intake, which can be done in an arbitrary nonequilibrium way e.g. combustion of fuel. Then the engine performs the work and returns to the initial state. We distinguish two general classes of engines where the working body first equilibrates within itself and then performs the work (ergodic engine) or when it performs the work before equilibrating (non-ergodic engine). We show that in both cases the second law of thermodynamics limits their efficiency. For ergodic engines we find a rigorous upper bound for the efficiency, which is strictly smaller than the equivalent Carnot efficiency. I.e. the Carnot efficiency can be never achieved in single reservoir heat engines. For non-ergodic engines the efficiency can be higher and can exceed the equilibrium Carnot bound. By extending the fundamental thermodynamic relation to nonequilibrium processes, we find a rigorous thermodynamic bound for the efficiency of both ergodic and non-ergodic engines and show that it is given by the relative entropy of the nonequilibrium and initial equilibrium distributions. These results suggest a new general strategy for designing more efficient engines. We illustrate our ideas by using simple examples.     

周期性双势垒锯齿势中温差驱动的布朗热机

研究了周期性双势垒锯齿势中, 布朗粒子在外力作用下沿空间坐标方向交替地和高、低温热库接触构成的布朗热机的热力学性能. 考虑布朗粒子动能的变化以及高、 低温库之间热漏的存在, 通过数值计算分析势垒高度、势比、外力等参数对布朗热机效率的影响. 研究表明：当考虑热漏时, 布朗热机始终是不可逆的, 效率小于卡诺效率; 并且当热漏很小时, 势比的增大在一定程度上可提高布朗热机的效率; 其功率与效率之间的关系曲线为闭合线. 当不考虑热漏时, 其功率与效率之间的关系曲线为开型线, 但由于布朗粒子动能的变化引起的不可逆热流, 热机的效率依然小于卡诺效率. 关键词： 布朗热机 双势垒锯齿势 热漏 热力学性能     

Carnot cycles in general relativity

Classical thermodynamics has been developed with the assumption that, either no gravitational fields are present in the thermodynamic systems, or that the fields act on the Newtonian mass of the systems only and not on any other kind of internal energy like heat. In order to find the exact thermodynamic relations for systems with gravitational fields, the wellknown Carnot cycles are used, taking into account the action of gravitation. The gravitation is described by general relativity. The Carnot efficiency is calculated in the case of stationary fields. Temperature for general relativistic systems can be defined with the help of Kelvin's principle analogously to classical thermodynamics, and the Carnot efficiency can then be expressed with temperatures instead of heat energies. In the case of strong gravitational fields, the Carnot efficiency can become equal to one even if the temperatures are both different from zero. Thermodynamic equilibrium can be expressed by using the Carnot efficiency, and it can be proved that for equilibrium the Tolman relation = constantholds quite generally for systems with stationary gravitational fields.Presented at the International Conference on Gravitation and Relativity, Copenhagen, July 1971.For 1969–71 on leave of absence at the Center for Relativity Theory, University of Texas at Austin, Austin, Texas, as a Faculty Associate supported by the National Science Foundation (Grant No. GU-1598).     

Consistency of optimizing finite-time Carnot engines with the low-dissipation model in the two-level atomic heat engine

The efficiency at the maximum power (EMP) for finite-time Carnot engines established with the low-dissipation model, relies significantly on the assumption of the inverse proportion scaling of the irreversible entropy generation ΔS^(ir) on the operation time τ, i.e. ΔS^(ir) ∝ 1/τ. The optimal operation time of the finite-time isothermal process for EMP has to be within the valid regime of the inverse proportion scaling. Yet, such consistency was not tested due to the unknown coefficient of the 1/τ-scaling. In this paper, we reveal that the optimization of the finite-time two-level atomic Carnot engines with the low-dissipation model is consistent only in the regime of η_C < 2(1 − δ)/(1 + δ), where η_C is the Carnot efficiency, and δ is the compression ratio in energy level difference of the heat engine cycle. In the large-η_C regime, the operation time for EMP obtained with the low-dissipation model is not within the valid regime of the 1/τ-scaling, and the exact EMP of the engine is found to surpass the well-known bound η₊ = η_C/(2 − η_C).     

Quantum point contacts as heat engines

The efficiency of macroscopic heat engines is restricted by the second law of thermodynamics. They can reach at most the efficiency of a Carnot engine. In contrast, heat currents in mesoscopic heat engines show fluctuations. Thus, there is a small probability that a mesoscopic heat engine exceeds Carnot's maximum value during a short measurement time. We illustrate this effect using a quantum point contact as a heat engine. When a temperature difference is applied to a quantum point contact, the system may be utilized as a source of electrical power under steady state conditions. We first discuss the optimal working point of such a heat engine that maximizes the generated electrical power and subsequently calculate the statistics for deviations of the efficiency from its most likely value. We find that deviations surpassing the Carnot limit are possible, but unlikely.     

Reprint of : Quantum point contacts as heat engines

The efficiency of macroscopic heat engines is restricted by the second law of thermodynamics. They can reach at most the efficiency of a Carnot engine. In contrast, heat currents in mesoscopic heat engines show fluctuations. Thus, there is a small probability that a mesoscopic heat engine exceeds Carnot's maximum value during a short measurement time. We illustrate this effect using a quantum point contact as a heat engine. When a temperature difference is applied to a quantum point contact, the system may be utilized as a source of electrical power under steady state conditions. We first discuss the optimal working point of such a heat engine that maximizes the generated electrical power and subsequently calculate the statistics for deviations of the efficiency from its most likely value. We find that deviations surpassing the Carnot limit are possible, but unlikely.     

Effects of impurity on the entanglement of the three-qubit Heisenberg XXX spin chain

We investigate the entanglement of the three-qubit Heisenberg XXX chain in the presence of impurity and obtain the analytical expressions of the concurrence C. It is found that for impurity entanglement, C appears only when J1 > J for J > 0, and J1 > 0 for J < 0, and in these two regions C increases with the increase of J1, so is the critical temperature Tc. When J1 >>|J| , C reaches its maximum value 0.5 and Tc reaches the asymptotic value Tc = 3.41448J1. For entanglement between the normal lattices, C appears only when J > 0 and 2J < J1 < J, and initially increases with the increase of J1 and arrives at the maximum value Cmax = (e4JIT-3)/(e4JIT+3) before it decays to zero gradually, so is the critical temperature Tc with, however, the maximum value Tcmax = 4J/ln3.     

Reversible Carnot cycle outside a black hole

A Carnot cycle outside a Schwarzschild black hole is investigated in detail. We propose a reversible Carnot cycle with a black hole being the cold reservoir. In our model, a Carnot engine operates between a hot reservoir with temperature T₁ and a black hole with Hawking temperature T_H. By naturally extending the ordinary Carnot cycle to the black hole system, we show that the thermal efficiency for a reversible process can reach the maximal efficiency 1-T_H/T₁. Consequently, black holes can be used to determine the thermodynamic temperature by means of the Carnot cycle. The role of the atmosphere around the black hole is discussed. We show that the thermal atmosphere provides a necessary mechanism to make the process reversible.     

能造出功率和效率都高的热机吗?——有限时间热力学的发展与展望

在热力学中,功率和效率是衡量热机性能的两个主要参数.根据经典热力学,可逆热机效率的上限是卡诺效率,但相应的功率为零.这是因为卡诺效率的实现依赖于时间无穷长的准静态假设.因此,如何根据实际需求,在保证热机功率前提下提高热机效率成为热力学一个重要的科学挑战问题.在20世纪上半叶应运而生的有限时间热力学,今天得到了蓬勃发展,...     

Current,maximum power and optimized efficiency of a Brownian heat engine

A microscopic heat engine is modeled as a Brownian particle in a sawtooth potential (with load) moving through a highly viscous medium driven by the thermal kick it gets from alternately placed hot and cold heat reservoirs. We found closed form expression for the current as a function of the parameters characterizing the model. Depending on the values these model parameters take, the engine is also found to function as a refrigerator. Expressions for the efficiency as well as for the refrigerator performance are also reported. Study of how these quantities depend on the model parameters enabled us in identifying the points in the parameter space where the engine performs with maximum power and with optimized efficiency. The corresponding efficiencies of the engine are then compared with those of the endoreversible and Carnot engines.Received: 28 December 2003, Published online: 28 May 2004PACS: 05.40.Jc Brownian motion - 05.60.-k Transport processes - 05.70.-a ThermodynamicsMesfin Asfaw: Present address: Max Planck Institute of Colloids and Interfaces, 14424 Potsdam, Germany     

奇异夸克物质的夸克质量密度温度相关模型(英文)

在夸克质量密度相关模型处理奇异夸克物质滴时 ,会发现其半径随温度增加而变小 .为克服这一困难 ,我们通过使口袋常数 B温度参数化 ,引入了夸克质量密度温度相关模型 .在这一模型中 ,B=B0 [1 - a(T/Tc) +b(T/Tc) 2 ],文章中讨论了参数 a,b的取法. It is found that the radius for a stable strangelet is a decreasing function of temperature in quark mass density- dependent model. To overcome this difficulty, we extend this model to quark mass density- and temperature- dependent model in which the vacuum energy density at zero baryon density limit B depends on temperature. An ansatz B=B 0[1-a(T/T c )+b(T/T c ) 2] is introduced and the regions for the best choice of the parameters are studied.     

Carnot efficiency: Why?

In 1824, Carnot proposed a cycle operating on reversibility principles. He proved that there exists an upper limit of the efficiency of this cycle and this limit is also the upper limit for any real process. The irreversibility related to the finite-time and the finite-size constraints are fundamental for the optimization of any real thermodynamic system. It has been pointed out how fundamental is the interaction between any open system and its surroundings. The meaning of the Carnot efficiency is that even in the ideal condition, when there is no dissipation, there exists something that does not allow the system to convert all the energies absorbed in work. The aim of this paper is to show why this happens, starting from a variational approach of thermodynamics.     

Scaling hot-electron generation to high-power, kilojoule-class laser-solid interactions

Thin-foil targets were irradiated with high-power (1 ≤ P(L) ≤ 210 TW), 10-ps pulses focused to intensities of I>10(18) W/cm(2) and studied with K-photon spectroscopy. Comparing the energy emitted in K photons to target-heating calculations shows a laser-energy-coupling efficiency to hot electrons of η(L-e) = 20 ± 10%. Time-resolved x-ray emission measurements suggest that laser energy is coupled to hot electrons over the entire duration of the incident laser drive. Comparison of the K-photon emission data to previous data at similar laser intensities shows that η(L-e) is independent of laser-pulse duration from 1 ≤ τ(p) ≤ 10 ps.     

带有Dzyaloshinski-Mariya相互作用的两比特纠缠量子Otto热机和量子Stirling热机

研究了以带有Dzyaloshinski-Mariya(DM)相互作用的两比特自旋体系为工质的量子纠缠Otto热机和量子Stirling热机.两种不同热机在各自的循环过程中,通过保持其他参量不变,只有DM相互作用发生改变,从而分析热机循环中DM相互作用与热传递、做功以及效率等热力学量之间的关系.研究结果表明:DM相互作用对两种热机的基本量子热力学量都具有重要的影响,但量子Stirling热机由于回热器的使用,其循环效率会大于量子Otto纠缠热机的效率,甚至会超过Carnot效率;得到了量子Otto纠缠热机和量子Stirling热机做正功的条件.因此,在这两个纠缠体系中,热力学第二定律都依然成立.     

On the thermodynamic limit of photovoltaic energy conversion

An infinite stack ofp—n junctions with smoothly varying bandgap from ∞ to 0 is considered. AnI —V characteristic is derived, which is more correct than the classical exponential characteristic. It is shown that open-circuit operation is a reversible process and leads to the Carnot efficiency, if one defines the efficiency in the way that is usual in the theory of thermodynamic engines. If instead one uses the definition of efficiency usual in photovoltaics, open-circuit mode gives rise to zero efficiency. Then operation at maximum efficiency equals operation at maximum power and is not reversible.     

加速器驱动快/热耦合次临界系统的概念设计

对加速器驱动快／热耦合次临界系统进行了概念设计研究。在该系统中,内区的快包层和外区的热包层是相互独立的,快、热包层之间为空腔和B4C包层以实现单向耦合。快包层装以合金（MA＋Pu）Zr为燃料,热包层初始循环装以氧化物（Th＋Pu）O₂为燃料,平衡循环装以（Th＋^233 U＋Pu）O2为燃料。^99Tc,^129I和^135Cs分别以单质、NaI和CsCl的形式装入热包层。该系统具有较高的能量放大倍数、嬗变效率和燃料转换比:系统能量放大系数不低于320;锕系元素（MA）和裂变产物（FP）的嬗变支持比分别为1个和2个压水堆;热包层的燃料转换比为0．715。 Accelerator driven coupled fast/thermal subcritical system is conceptually designed. In the system, the inner/fast blanket and the outer/thermal blanket are separated each other by large vacuum and B4C coating for on edirection coupling. The metal type fuel （MA ＋ Pu）Zr is loaded into the fast blanket. The oxide type fuels （Th ＋ Pu） O2 and （Th ＋ ^233U ＋ Pu）O2 are loaded into the thermal blanket during the initial cycle and the equilibrium cycle, respectively. ^99Tc, ^129I and ^135Cs are loaded respectively in the form of pure technetium metal, sodium iodide and cesium chlorine into the thermal blanket. The system has good transmutation efficiency, high energy amplification factor and good fuel conversion ability: the energy amplification factor is above 320; the transmutation support ratios of MA and FP are about 1.0 and 2.0 PWRs respectively; the fuel conversion ratio in the thermal blanket is about 0. 715.