The paper develops the dynamics and thermodynamics of Stirling engines that run with temperature differences below 100 0C. The working gas pressure is analytically expressed using an alternative thermodynamic cycle. The shaft dynamics is studied using its rotational equation of motion. It is found that the initial volumes of the cold and hot working gas play a non-negligible role in the functioning of the engine.
A Stirling engine made of a colloidal particle in contact with a nonequilibrium bath is considered and analyzed with the tools of stochastic energetics. We model the bath by non Gaussian persistent noise acting on the colloidal particle. Depending on the chosen definition of an isothermal transformation in this nonequilibrium setting, we find that either the energetics of the engine parallels that of its equilibrium counterpart or, in the simplest case, that it ends up being less efficient. Persistence, more than non Gaussian effects, are responsible for this result.
Reaching maximum efficiency in quantum Stirling engines using multilayer graphene
Pontificia Universidad Católica de Valparaíso（天主教瓦尔帕莱索大学）；Universidad Técnica Federico Santa María（费德里科·圣玛丽亚技术大学）；Universidade Federal do Rio de Janeiro（里约热内卢联邦大学）
We propose a quantum Stirling heat engine with an ensemble of harmonic oscillators as the working medium. We show that the efficiency of the harmonic oscillator quantum Stirling heat engine (HO-QSHE) at a given frequency can be maximized at a specific ratio of the temperatures of the thermal reservoirs. In the low temperature or equivalently high frequency limit of the harmonic oscillators, the efficiency of the HO-QSHE approaches the Carnot efficiency. Further, we analyse quantum Stirling heat engine with an ensemble of particle in box quantum systems as the working medium. Here both work and…
This paper describes simple modifications to a demonstration Stirling engine that allows one to make quantitative measurements of the Stirling cycle. First, we describe measurements of the $P$-$V$ diagram using an inexpensive pressure sensor and a common photogate. Then, as a supplement, the engine was run as a refrigerator by using a rotary tool to turn the flywheel of the engine. A small, but measurable, temperature difference developed across the body of the engine.
Quantum Level-Crossing Induced by Anisotropy in Spin-1 Heisenberg Dimers: Applications to Quantum Stirling Engines
Pontificia Universidad Católica de Valparaíso（智利天主教瓦尔帕莱索大学）；Universidad Técnica Federico Santa María（费德里科·圣玛丽亚理工大学）；Fluminense Federal University（弗鲁米嫩塞联邦大学）；Western Bahia Federal University（巴伊亚西部联邦大学）
The low-temperature-differential (LTD) Stirling heat engine technology constitutes one of the important sustainable energy technologies. The basic question of how the rotational motion of the LTD Stirling heat engine is maintained or lost based on the temperature difference is thus a practically and physically important problem that needs to be clearly understood. Here, we approach this problem by proposing and investigating a minimal nonlinear dynamic model of an LTD kinematic Stirling heat engine. Our model is described as a driven nonlinear pendulum where the motive force is the temperature…
Low-temperature-differential (LTD) Stirling heat engines are able to operate with a small temperature difference between low-temperature heat reservoirs that exist in our daily lives, and thus they are considered to be an important sustainable energy technology. The author recently proposed a nonlinear dynamics model of an LTD kinematic Stirling heat engine to study the rotational mechanism of the engine [Y. Izumida, EPL \textbf{121}, 50004 (2018)]. This paper presents our study of the nonequilibrium thermodynamics analysis of this engine model, where a load torque against which the engine doe…
Colloidal heat engines are paradigmatic models to understand the conversion of heat into work in a noisy environment - a domain where biological and synthetic nano/micro machines function. While the operation of these engines across thermal baths is well-understood, how they function across baths with noise statistics that is non-Gaussian and also lacks memory, the simplest departure from equilibrium, remains unclear. Here we quantified the performance of a colloidal Stirling engine operating between an engineered \textit{memoryless} non-Gaussian bath and a Gaussian one. In the quasistatic lim…
Nonequilibrium thermodynamics of populations of weakly-coupled low-temperature-differential Stirling engines with synchronous and asynchronous transitions
We develop an alternative thermodynamic cycle for the Stirling machine, where the polytropic process plays a central role. Analytical expressions for pressure and temperatures of the working gas are obtained as a function of the volume and the parameter which characterizes the polytropic process. This approach achieves a closer agreement with the experimental pressure-volume diagram and can be adapted to any type of the Stirling engine.
Effects of Magnetic Anisotropy on 3-Qubit Antiferromagnetic Thermal Machines
Pontificia Universidad Católica de Valparaíso（天主教瓦爾帕萊索大學）；Universidad Técnica Federico Santa María（費德里科·聖塔瑪麗亞理工大學）；Millennium Nucleus in NanoBioPhysics (NNBP)（納米生物物理千年核）；Universidad Mayor（馬約爾大學）；Ohio University（俄亥俄大學）
Artificial micro heat engines are prototypical models to explore and elucidate the mechanisms of energy transduction in a regime that is dominated by fluctuations [1-2]. Micro heat engines realized hitherto mimicked their macroscopic counterparts and operated between reservoirs that were effectively thermal [3-7]. For such reservoirs, temperature is a well-defined state variable and stochastic thermodynamics provides a precise framework for quantifying engine performance [8-9]. It remains unclear whether these concepts readily carry over to situations where the reservoirs are out-of-equilibriu…
A typical model for a gyrating engine consists of an inertial wheel powered by an energy source that generates an angle-dependent torque. Examples of such engines include a pendulum with an externally applied torque, Stirling engines, and the Brownian gyrating engine. Variations in the torque are averaged out by the inertia of the system to produce limit cycle oscillations. While torque generating mechanisms are also ubiquitous in the biological world, where they typically feed on chemical gradients, inertia is not a property that one naturally associates with such processes. In the present wo…
The purpose of this work is to present the concept of an autonomous Stirling-like engine powered by anisotropy of thermodynamic fluctuations. Specifically, simultaneous contact of a thermodynamic system with two heat baths along coupled degrees of freedom generates torque and circulatory currents -- an arrangement referred to as a Brownian gyrator. The embodiment that constitutes the engine includes an inertial wheel to sustain rotary motion and average out the generated fluctuating torque, ultimately delivering power to an external load. We detail an electrical model for such an engine that c…
Bosonic Working Media in a Frustrated Rhombi Chain: Otto and Stirling Cycles from Flat Bands, Caging, and Flux Control
Facultad de Ingeniería, Universidad San Sebastián（圣塞巴斯蒂安大学工程学院）；Departamento de Física, Universidad Técnica Federico Santa María（智利技术费德里科·萨马拉大学物理系）；Department of Physics, Universitat Autònoma de Barcelona（巴塞罗那自治大学物理系）；Instituto de Física, Pontificia Universidad Católica de Valparaíso（天主教瓦尔帕莱索大学物理研究所）；Physical and Computational Sciences,Pacific Northwest National Laboratory（太平洋西北国家实验室物理与计算科学部）；Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile（智利大学物理与数学科学学院物理系）
The Carnot theorem, one expression of the second law of thermodynamics, places a fundamental upper bound on the efficiency of heat engines operating between two heat baths. The Carnot theorem can be stated in a more generalized form for heat engines operating with multiple heat baths, where the maximum efficiency is achieved for reversible heat engines operating quasistatically between two heat baths. In this study, we determine the irreversible efficiency of heat engines operating with multiple heat baths in a linear response regime, i.e., under small temperature differences and a slow variat…
We study a quantum Stirling cycle which extracts work using quantized energy levels of a potential well. The work and the efficiency of the engine depend on the length of the potential well, and the Carnot efficiency is approached in a low temperature limiting case. We show that the lack of information about the position of the particle inside the potential well can be converted into useful work without resorting to any measurement. In the low temperature limit, we calculate the amount of work extractable from distinguishable particles, fermions, and bosons.
We study a two-level system controlled in a discrete feedback loop, modeling both the system and the controller in terms of stochastic Markov processes. We find that the extracted work, which is known to be bounded from above by the mutual information acquired during measurement, has to be compensated by an additional energy supply during the measurement process itself, which is bounded by the same mutual information from below. Our results confirm that the total cost of operating an information engine is in full agreement with the conventional second law of thermodynamics. We also consider th…
The autonomous heat engine is a model system of autonomous nonequilibrium systems like biological cells, exploiting nonequilibrium flow for operations. As the Carnot engine has essentially contributed to the equilibrium thermodynamics, autonomous heat engine is expected to play a critical role in the challenge of constructing nonequilibrium thermodynamics. However, the high complexity of the engine involving an intricate coupling among heat, gas flow, and mechanics has prevented simple modeling. Here, we experimentally characterized the nonequilibrium dynamics and thermodynamics of a low-tempe…
We study the optimal performance of an endoreversible quantum dot heat engine, in which the heat transfer between the system and baths is mediated by qubits, operating under the conditions of a trade-off objective function known as maximum efficient power function defined by the product of power and efficiency of the engine. First, we numerically study the optimization of the efficient power function for the engine under consideration. Then, we obtain some analytic results by applying hightemperature limit and compare the performance of the engine at maximum efficient power functionto the engi…
We formulate the work output and efficiency for linear irreversible heat engines working between a finite-sized hot heat source and an infinite-sized cold heat reservoir until the total system reaches the final thermal equilibrium state with a uniform temperature. We prove that when the heat engines operate at the maximum power under the tight-coupling condition without heat leakage the work output is just half of the exergy, which is known as the maximum available work extracted from a heat source. As a consequence, the corresponding efficiency is also half of its quasistatic counterpart.
We investigate fluctuations of output work for a class of Stirling heat engines with working fluid composed of interacting units and compare these fluctuations to an average work output. In particular, we focus on engine performance close to a critical point where Carnot's efficiency may be attained at a finite power as reported in [M. Campisi and R. Fazio, Nat. Commun. 7, 11895 (2016)]. We show that the variance of work output per cycle scales with the same critical exponent as the heat capacity of the working fluid. As a consequence, the relative work fluctuation diverges unless the output w…
In order to establish better performance compromises between the process functionals of a heat engine, in the context of finite time thermodynamics (FTT), we propose some generalizations for the well known Efficient Power function through certain variables called <<Generalization Parameters>>. These generalization proposals show advantages in the characterization of operation modes for an endoreversible heat engine model. In particular, with introduce the k-Efficient Power regime. For this objective function we find the performance of the operation of some power plants through the parameter k.…
Ideal heat engine cycles at maximal efficiency -- the ideal gas and beyond
University of Maryland, College Park（马里兰大学帕克分校）；University of Maryland, Baltimore County（马里兰大学巴尔的摩郡分校）；Quantum Science Institute, University of Maryland, Baltimore County（马里兰大学巴尔的摩郡分校量子科学研究所）；National Quantum Laboratory（国家量子实验室）
We discuss the efficiency of a heat engine operating in a nonequilibrium steady state maintained by two heat reservoirs. Within the general framework of linear irreversible thermodynamics we derive a universal upper bound on the efficiency of the engine operating at arbitrary fixed power. Furthermore, we show that a slight decrease of the power below its maximal value can lead to a significant gain in efficiency. The presented analysis yields the exact expression for this gain and the corresponding upper bound.
Stochastic thermodynamics has revolutionized our understanding of heat engines operating in finite time. Recently, numerous studies have considered the optimal operation of thermodynamic cycles acting as heat engines with a given profile in thermodynamic space (e.g. $P-V$ space in classical thermodynamics), with a particular focus on the Carnot engine. In this work, we use the lens of thermodynamic geometry to explore the full space of thermodynamic cycles with continuously-varying bath temperature in search of optimally shaped cycles acting in the slow-driving regime. We apply classical isope…
We investigate a model for a Stirling-like engine consisting of a passive Brownian particle confined by a harmonic potential and interacting with a suspension of active Brownian particles that self-propel in a viscous solvent, which cyclically operates under isothermal conditions by means of temporal variations of the trap stiffness and the self-propulsion speed of the active particles. We derive an effective stochastic equation of motion of the trapped Brownian particle, which includes a friction memory kernel as well as thermal and active fluctuating forces due to its coupling with the activ…
Miniaturized heat engines constitutes a fascinating field of current research. They are being studied theoretically as well as experimentally, with experiments involving colloidal particles and harmonic traps and even bacterial baths acting like thermal baths. They are interesting to study because usual equilibrium thermodynamic notions can not be applied directly to these systems. These systems are micron sized or even smaller and they are subjected to laud thermal fluctuations. Thus one needs to study the behavior of such systems in terms of these fluctuations. Average thermodynamic quantiti…
The efficiency at maximum power has been investigated extensively, yet the practical control scheme to achieve it remains elusive. We fill such gap with a stepwise Carnot-like cycle, which consists the discrete isothermal process (DIP) and adiabatic process. With DIP, we validate the widely adopted assumption of \mathscr{C}/t relation of the irreversible entropy generation S^{(\mathrm{ir})}, and show the explicit dependence of the coefficient \mathscr{C} on the fluctuation of the speed of tuning energy levels as well as the microscopic coupling constants to the heat baths. Such dependence allo…
We investigate the thermodynamic efficiency of sub-micro-scale heat engines operating under the conditions described by over-damped stochastic thermodynamics. We prove that at maximum power the efficiency obeys for constant isotropic mobility the universal law $η=2\,η_{C}/(4-η_{C})$ where $η_{C}$ is the efficiency of an ideal Carnot cycle. The corresponding power optimizing protocol is specified by the solution of an optimal mass transport problem. Such solution can be determined explicitly using well known Monge--Ampère--Kantorovich reconstruction algorithms. Furthermore, we show that the sam…
The constraint relation for efficiency and power is crucial to design optimal heat engines operating within finite time. We find a universal constraint between efficiency and output power for heat engines operating in the low-dissipation regime. Such constraint is validated with an example of Carnot-like engine. Its microscopic dynamics is governed by the master equation. Based on the master equation, we connect the microscopic coupling strengths to the generic parameters in the phenomenological model. We find the usual assumption of low-dissipation is achieved when the coupling to thermal env…
The work provides an overview on some recent advances in the area of quantum thermodynamics and quantum heat engines. A particular emphasis is put on the possibility of constructing finite time quantum cycles and adiabatic shortcuts. We discuss in details the particular quantum heat engines operating with a multiferroic working substance.
We show that a Carnot cycle operating between a positive canonical-temperature bath and a negative canonical-temperature bath has efficiency equal to unity. It follows that a negative canonical-temperature cannot be identified with an absolute temperature. We illustrate this with a spin in a varying magnetic field.
The construction of efficient thermal engines operating at finite times constitutes a fundamental and timely topic in nonequilibrium thermodynamics. We introduce a strategy for optimizing the performance of Brownian engines, based on a collisional approach for unequal interaction times between the system and thermal reservoirs. General (and exact) expressions for thermodynamic properties and their optimized values are obtained, irrespective of the driving forces, asymmetry, the temperatures of reservoirs and protocol to be maximized. Distinct routes for the engine optimization, including maxim…
We study a driven harmonic oscillator operating an Otto cycle between two thermal baths of finite size. By making extensive use of the tools of Gaussian quantum mechanics, we directly simulate the dynamics of the engine as a whole, without the need to make any approximations. This allows us to understand the non-equilibrium thermodynamics of the engine not only from the perspective of the working medium, but also as it is seen from the thermal baths' standpoint. For sufficiently large baths, our engine is capable of running a number of ideal cycles, delivering finite power while operating very…
We consider a finite-time Otto engine operating on a quantum harmonic oscillator and driven by shortcut-to-adiabaticity (STA) techniques to speed up its cycle. We study its efficiency and power when internal friction, time-averaged work, and work fluctuations are used as quantitative figures of merit, showing that time-averaged efficiency and power are useful cost functions for the characterization of the performance of the engine. We then use the minimum allowed time for validity of STA protocol relation to establish a physically relevant bound to the efficiency at maximum power of the STA-dr…
A 1D Josephson junction loop, doped with a spin-flipper and attached to two thermal reservoirs, operates as a heat engine or a refrigerator, a Joule pump, or even a cold pump. When operating as a quantum heat engine, the efficiency of this device exceeds that of some recent Josephson heat engine proposals. Further, as a quantum refrigerator, the coefficient of performance of this device is much higher than previously proposed Josephson junction-based refrigerators. In addition, this device can be tuned from engine mode to refrigerator mode or any other mode, i.e., Joule pump or cold pump, by e…
