Massimiliano Esposito, Ryoichi Kawai, Katja Lindenberg, Christian Van den Broeck
We evaluate the efficiency at maximum power of a quantum-dot Carnot heat engine. The universal value of the coefficients at the linear and quadratic order in the temperature gradient are reproduced. Curzon-Ahlborn efficiency is recovered in the limit of weak dissipation.
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The present work investigates the generalized extreme bounds of the coefficient of performance (COP) for the power law dissipative Carnot-like refrigerator in the presence of non-adiabatic dissipation under $χ$ and $\dotΩ$ optimization criteria. The lower and upper bounds of the COP for the low dissipation Carnot-like refrigerator under $χ$ and $\dotΩ$ optimization criteria are obtained with power law dissipation level $δ=1$. The comparative analysis of the extreme bounds of COP at optimized $\dot{Ω}$ and $χ$ figure of merit shows the lower bound of the $\dotΩ$ optimized COP is always higher t…
In the present work, a power law dissipative Carnot like heat engine cycle of two irreversible isothermal and two irreversible adiabatic processes with finite time non-adiabatic dissipation is considered and the efficiency under two optimization criteria $\dotΩ$ figure of merit and efficient power, $χ_{ep}$ is studied. The generalized extreme bounds of the optimized efficiency under the above said optimization criteria are obtained. The lower and upper bounds of the efficiency for the low dissipation Carnot-like heat engine under these optimization criteria are obtained with dissipation level …
The condition for stationary engines to attain the Carnot efficiency in and beyond the linear response regime is investigated. We find that this condition for finite-size engines is significantly different from that for macroscopic engines in the thermodynamic limit. For the case of finite-size engines, the tight-coupling condition in the linear response regime directly implies the attainability of the Carnot efficiency beyond the linear response regime. Contrary to this, for the case of macroscopic engines in the thermodynamic limit, there are three types of mechanisms to attain the Carnot ef…
The maximum efficiency of autonomous engines with finite chemical potential difference is investigated. We show that without a particular type of singularity autonomous engines cannot attain the Carnot efficiency. In addition, we demonstrate that a special autonomous engine with the singularity attains the Carnot efficiency even if it is macroscopic. Our results clearly illustrate that the singularity plays a crucial role for the maximum efficiency of autonomous engines.
Considering ideal paramagnetic medium, in this paper we deduced an expression for the thermal efficiency of Carnot heat engine with a paramagnetic gas as working substance. We found that the efficiency depends on the limits of maximum and minimal temperature imposed on the Carnot cycle, as in the ideal gas, photon gas and variable Chaplygin gas.
The efficient conversion of thermal energy to mechanical work by a heat engine is an ongoing technological challenge. Since the pioneering work of Carnot, it is known that the efficiency of heat engines is bounded by a fundamental upper limit, the Carnot limit. Theoretical studies suggest that heat engines may be operated beyond the Carnot limit by exploiting stationary, non-equilibrium reservoirs that are characterized by a temperature as well as further parameters. In a proof-of-principle experiment, we demonstrate that the efficiency of a nano-beam heat engine coupled to squeezed thermal no…
In order to build a quantum analog of traditional Carnot engine, a common choice is replacing the two thermodynamic adiabatic processes with two quantum mechanical adiabatic processes. In general, such quantum Carnot engine has six strokes. We analyze the efficiency of such six-stroke quantum Carnot engine in a perturbative way.
We study the efficiency at maximum power of non-adiabatic dissipative (internally dissipative friction in finite time adiabatic processes) Carnot-like heat engines operate in finite time under the power law dissipation regime. We find that the non-adiabatic dissipation does not influence the universal minimum and maximum bounds on the efficiency at maximum power obtained in the generalized dissipative Carnot-like heat engines which does not take in to account the non-adiabatic dissipation.
The efficiency at maximum power (EMP) of irreversible Carnot-like heat engines is investigated based on the weak endoreversible assumption and the phenomenologically irreversible thermodynamics. It is found that the weak endoreversible assumption can reduce to the conventional one for the heat engines working at maximum power. Carnot-like heat engines are classified into three types (linear, superlinear, and sublinear) according to different characteristics of constitutive relations between the heat transfer rate and the thermodynamic force. The EMPs of Carnot-like heat engines are proved to b…
The Carnot-like heat engines are classified into three types (normal-, sub- and super-dissipative) according to relations between the minimum irreversible entropy production in the "isothermal" processes and the time for completing those processes. The efficiencies at maximum power of normal-, sub- and super-dissipative Carnot-like heat engines are proved to be bounded between $η_C/2$ and $η_C/(2-η_C)$, $η_C /2$ and $η_C$, 0 and $η_C/(2-η_C)$, respectively. These bounds are also shared by linear, sub- and super-linear irreversible Carnot-like engines [Tu and Wang, Europhys. Lett. 98, 40001 (20…
We study the maximum efficiency of a Carnot cycle heat engine based on a small system. It is revealed that due to the finiteness of the system, irreversibility may arise when the working substance contacts with a heat bath. As a result, there is a working-substance-dependent correction to the usual Carnot efficiency, which is valid only when the working substance is in the thermodynamic limit. We derives a general and simple expression for the maximum efficiency of a Carnot cycle heat engine in terms of the relative entropy. This maximum efficiency approaches the usual Carnot efficiency asympt…
In their work [J. Phys. A: Math. Gen. 33, 4427 (2000)], Bender, Brody, and Meister have shown by employing a two-state model of a particle confined in the one-dimensional infinite potential well that it is possible to construct a quantum-mechanical analog of the Carnot engine through the changes of both the width of the well and the quantum state in a specific manner. Here, a discussion is developed about realizing the maximum power of such an engine, where the width of the well moves at low but finite speed. The efficiency of the engine at the maximum power output is found to be universal ind…
The Carnot cycle imposes a fundamental upper limit to the efficiency of a macroscopic motor operating between two thermal baths. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors and some artificial micro-engines operate. As described by stochastic thermodynamics, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit. Despite its potential relevance for the development of a thermodynamics of small systems, an experimental study of micro…
Motivated by the recent work by Mandal and Jarzynski on autonomous Maxwell demon information engine, we have extended their model by introducing two different heat baths. The system (demon) is coupled to a memory register (tape) and a work source. The performance of the system depends on the interplay between these two sources along with the heat baths. We have found the system can act as an engine, refrigerator or an eraser. Even the combination of any two is possible in some parameter space. We have achieved the efficiency of the engine is greater than Carnot limit. The coefficient of perfor…
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 discuss the reversibility of Brownian heat engine. We perform asymptotic analysis of Kramers equation on Büttiker-Landauer system and show quantitatively that Carnot efficiency is inattainable even in a fully overdamping limit. The inattainability is attributed to the inevitable irreversible heat flow over the temperature boundary.
Geometric Formulation of Power-Efficiency Bounds in Carnot-like Engines
将卡诺类热机的功率-效率约束转化为归一化分支耗散平面上的几何优化问题，通过线性规划得到幂律耗散下的精确约束。
A quantum-mechanical analog of the Carnot engine reversibly working at vanishing temperature, shortly termed the quantum-mechanical Carnot engine, is discussed. A general formula for the efficiency of such an engine with an arbitrary confining potential is presented. Its expression is purely given in terms of the structure of the energy spectrum. Dependency of the efficiency on the form of a potential as an analog of the working material in thermodynamics implies nonuniversality of the engine. This may be due to the absence of the second-law-like principle in pure-state quantum mechanics.
Recent advances in experimental control of colloidal systems have spurred a revolution in the production of mesoscale thermodynamic devices. Functional "textbook" engines, such as the Stirling and Carnot cycles, have been produced in colloidal systems where they operate far from equilibrium. Simultaneously, significant theoretical advances have been made in the design and analysis of such devices. Here, we use methods from thermodynamic geometry to characterize the optimal finite-time, nonequilibrium cyclic operation of the parametric harmonic oscillator contact with a time-varying heat bath, …
We study the efficiency at maximum power, $η^*$, of engines performing finite-time Carnot cycles between a hot and a cold reservoir at temperatures $T_h$ and $T_c$, respectively. For engines reaching Carnot efficiency $η_C=1-T_c/T_h$ in the reversible limit (long cycle time, zero dissipation), we find in the limit of low dissipation that $η^*$ is bounded from above by $η_C/(2-η_C)$ and from below by $η_C/2$. These bounds are reached when the ratio of the dissipation during the cold and hot isothermal phases tend respectively to zero or infinity. For symmetric dissipation (ratio one) the Curzon…
Achieving the Carnot efficiency at finite power is a challenging problem in heat engines due to the trade-off relation between efficiency and power that holds for general heat engines. It is pointed out that the Carnot efficiency at finite power may be achievable in the vanishing limit of the relaxation times of a system without breaking the trade-off relation. However, any explicit model of heat engines that realizes this scenario for arbitrary temperature difference has not been proposed. Here, we investigate an underdamped Brownian Carnot cycle where the finite-time adiabatic processes conn…
A role of the superposition principle is discussed for the quantum-mechanical Carnot engine introduced by Bender, Brody, and Meister [J. Phys. A 33, 4427 (2000)]. It is shown that the efficiency of the engine can be enhanced by superposition of quantum states. A finite-time process is also discussed, and the condition of the maximum power output is presented. Interestingly, the efficiency at the maximum power is lower than that without superposition.
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 disc…
Stability is an important property of small thermal machines with fluctuating power output. We here consider a finite-time quantum Carnot engine based on a degenerate multilevel system and study the influence of its finite Hilbert space structure on its stability. We optimize in particular its relative work fluctuations with respect to level degeneracy and level number. We find that its optimal performance may surpass those of nondegenerate two-level engines or harmonic oscillator motors. Our results show how to realize high-performance, high-stability cyclic quantum heat engines.
The Carnot statement of the second law of thermodynamics poses an upper limit on the efficiency of all heat engines. Recently, it has been studied whether generic quantum features such as coherence and quantum entanglement could allow for quantum devices with efficiencies larger than the Carnot efficiency. The present study shows that this is not permitted by the laws of thermodynamics. In particular, we will show that rather the definition of heat has to be modified to account for the thermodynamic cost for maintaining coherence and entanglement. Our theoretical findings are numerically illus…
Entropy-based analysis of single-qubit Otto and Carnot heat engines
该研究基于熵基理论分析了单量子比特Otto和Carnot热机的效率，揭示了相干工作与熵生成对热机性能的影响。
Beyond the Carnot Limit in the Internal Cycles of a Quantum Heat Engine under Finite Heat Reservoirs
本文解析研究了耦合有限热库的微观量子热机卡诺循环，证明其内部循环可在不消耗额外量子资源的情况下超越标准卡诺极限，并揭示了有限热库热容量对最大效率和功率输出的关键作用。
The Anyonic Quantum Carnot Engine
本文研究以二维任意子为介质的量子卡诺热机，推导出其效率的显式表达式，为探索小尺度量子系统的热力学及从量子统计中提取机械功提供了新途径。
Efficiency at maximum power of a Carnot quantum information engine
本文针对量子信息引擎，提出了广义有限时间Carnot循环，在低耗散区间优化功率输出，推导出适用于任意工作介质的最大功率效率通用公式，并研究了弱能量测量下qubit信息引擎的最优性能。
We study the optimal performance of Carnot-like heat engines working in low dissipation regime using the product of the efficiency and the power output, also known as the efficient power, as our objective function. Efficient power function represents the best trade-off between power and efficiency of a heat engine. We find lower and upper bounds on the efficiency in case of extreme asymmetric dissipation when the ratio of dissipation coefficients at the cold and the hot contacts approaches, respectively, zero or infinity. In addition, we obtain the form of efficiency for the case of symmetric …
In this work an example of a cyclic engine based on a quantum-mechanical properties of the strongly non linear quantum oscillator described by the Poschl-Teller [PT] model is examined. Using the [PT] model as shown in our earlier works [1-4], a quantum-mechanical analog of Carnot cycle (i.e quantum heat engine) has been constructed through the changes of both, the width L of the well and its quantum state. This quantum heat engine has a cycle consisting of adiabatic and isothermal quantum processes. The efficiency of the quantum engine based on the Poschl-Teller-like potential is derived and i…
Information-Assisted Carnot Engine Surpasses Standard Thermodynamic Bounds
本文提出卡诺信息机，定量揭示信息与热机性能的关系，证明其可超越标准卡诺效率并实现100%效率，并用自旋-1/2系统和囚禁离子方案加以验证。
A heat engine operating in the one-shot finite-size regime, where systems composed of a small number of quantum particles interact with hot and cold baths and are restricted to one-shot measurements, delivers fluctuating work. Further, engines with lesser fluctuation produce a lesser amount of deterministic work. Hence, the heat-to-work conversion efficiency stays well below the Carnot efficiency. Here we overcome this limitation and attain Carnot efficiency in the one-shot finite-size regime, where the engines allow the working systems to simultaneously interact with two baths via the semi-lo…
Revisiting Endo-reversible Carnot engine: Extending the Yvon engine
本文重新审视内可逆卡诺机，扩展了Yvon机模型，揭示了其与CA机在稳态和循环形式上的等价性，为热力学教学提供了示例。
The Carnot heat engine sets an upper bound on the efficiency of a heat engine. As an ideal, reversible engine, a single cycle must be performed in infinite time, and so the Carnot engine has zero power. However, there is nothing in principle forbidding the existence of a heat engine whose efficiency approaches that of Carnot while maintaining finite power. Such an engine must have very special properties, some of which have been discussed in the literature, in various limits. While recent theorems rule out a large class of engines from maintaining finite power at exactly the Carnot efficiency,…
The efficiency at maximum power output of linear irreversible Carnot-like heat engines is investigated based on the assumption that the rate of irreversible entropy production of working substance in each "isothermal" process is a quadratic form of heat exchange rate between the working substance and the reservoir. It is found that the maximum power output corresponds to minimizing the irreversible entropy production in two "isothermal" processes of the Carnot-like cycle, and that the efficiency at maximum power output has the form as $η_{mP}={η_C}/(2-γη_C)$ where $η_C$ is the Carnot efficienc…
Power-efficiency-stability trade-off in quantum information engines
该研究聚焦有限时间量子Carnot信息引擎的功率-效率-稳定性权衡，通过解析计算输出功的均值与方差，证明其可在有限功输出及涨落下达最大效率，且稳定性优于常规量子Carnot热机。
It was reported that, if and only if the specific heat, correlation length, and dynamical exponents $α, ν$ and $z$, fulfill the condition $α-zν>0$, the phase transitions can enable a quantum heat engine to approach Carnot efficiency at finite power. We start our analysis via a different approach in which the effects of interaction and fluctuations on the Hamiltonian of a trapped dilute Bose gas belonging to the same universality as $XY$ model. Based on models of quantum Otto heat engines, we find the general expression of the efficiency which includes the correction due to interaction and fluc…
We investigate the efficiency at maximum power (EMP) of irreversible quantum Carnot engines that perform finite-time cycles between two temperature tunable baths. The temperature form we adopt can be experimentally realized in squeezed baths in the high temperature limit, which makes our proposal of practical relevance. Focusing on low dissipation engines, we first generalize the pervious upper as well as lower bounds for the EMP to temperature tunable cases in which they are solely determined by a generalized Carnot limit. As an illustrative example, we then consider a minimal heat engine mod…
An Information-Theoretic Bound on Thermodynamic Efficiency and the Generalized Carnot's Theorem
本文推导了热机效率的更严格界限，适用于经典和量子热机，并展示了量子点与费米浴耦合的引擎可达到该界限，为实际能量收集设备提供设计原理。
A Minimal Model for Carnot Efficiency at Maximum Power
本研究提出一种最小热机模型，借助工作物质内的简并度等固有发散物理量，突破传统热机的功率-效率权衡，实现最大功率下的卡诺效率，为多体系统能量利用的集体优势提供新认知。
An analysis of efficiency and its bounds at maximum work output for Carnot-like heat engines is conducted. The heat transfer processes are described by the linear law with time-dependent heat conductance. The upper bound of efficiency is found to be the CA efficiency,and is independent of the time duration completing each process and the time-dependent conductance. We prove that even the working medium exchanges heat sufficiently with the heat reservoirs, the work which could be extracted is finite and limited. The optimal temperature profiles in the heat exchanging processes are also analyzed…
Approaching Carnot Efficiency at Finite Power in an Experimentally Feasible Quantum Heat Engine
研究热机在有限功率下逼近卡诺效率的问题，提出用超导电路热机模拟集体增强来实现，此结果规避了经典马尔可夫热机功率-效率权衡，连接抽象界限与具体平台，为量子器件设计提供途径。
We want to understand whether and to which extent the maximal (Carnot) efficiency for heat engines can be reached at a finite power. To this end we generalize the Carnot cycle so that it is not restricted to slow processes. We show that for realistic (i.e. not purposefully-designed) engine-bath interactions, the work-optimal engine performing the generalized cycle close to the maximal efficiency has a long cycle time and hence vanishing power. This aspect is shown to relate to the theory of computational complexity. A physical manifestation of the same effect is the Levinthal's paradox in the …
Carnot, Stirling, Ericsson stochastic heat engines: Efficiency at maximum power
本研究探讨了执行类Carnot、Stirling和Ericsson循环的随机热机，通过低耗散框架下的有限时间循环过程，求得了其在最大功率下的效率。
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 $ΔS^{(\mathrm{ir})}$ on the operation time $τ$, i.e., $ΔS^{(\mathrm{ir})}\propto1/τ$. 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, using a two-level atomic heat engine a…
The Carnot cycle is a prototype of ideal heat engine to draw mechanical energy from the heat flux between two thermal baths with the maximum efficiency, dubbed as the Carnot efficiency $η_{\mathrm{C}}$. Such efficiency can only be reached by thermodynamical equilibrium processes with infinite time, accompanied unavoidably with vanishing power - energy output per unit time. In real-world applications, the quest to acquire high power leads to an open question whether a fundamental maximum efficiency exists for finite-time heat engines with given power. We experimentally implement a finite-time C…
We study two-dimensional quantum Carnot engines of spherical symmetry by considering the case of a particle on the surface of a sphere of changing radius. The Carnot cycle is built allowing the state of the system to change with the specific constrains discussed in Bender's work for Carnot cycles. After studying the Carnot cycle, we maximize the output power and efficiency of the system to show that as it happens in one dimension systems:(i) the efficiency can be optimized; being its optimal value independent of the parameters describing the system and that the optimal output power at the opti…
There has been many studies on gases which obeys Van der Waal's equation of state. However there is no specific and direct studies of Van der Waal's gas which undergoes adiabatic processes are available in the undergraduate text books and also in literature. In an adiabatic process there is no heat energy exchange between the system and its surroundings. In this article, we find that the Van der Waal's equation for the adiabatic process as $\left(P+\frac{n^2a}{V^2}\right) \left(V-nb\right)^Γ=\mbox{constant}$, where $P$ is the pressure, $V$ is the volume, $n$ is the number of moles of the Van d…
The widely debated feasibility of thermodynamic machines achieving Carnot efficiency at finite power has been convincingly dismissed. Yet, the common wisdom that efficiency can only be optimal in the limit of infinitely-slow processes overlooks the dual scenario of infinitely-fast processes. We corroborate that efficient engines at divergent power output are not theoretically impossible, framing our claims within the theory of Stochastic Thermodynamics. We inspect the case of an electronic quantum dot coupled to three particle reservoirs to illustrate the physical rationale.
We analyse non-equilibrium Carnot-like cycles built with a colloidal particle in a harmonic trap, which is immersed in a fluid that acts as a heat bath. Our analysis is carried out in the overdamped regime. The cycle comprises four branches: two isothermal processes and two \textit{locally} adiabatic ones. In the latter, both the temperature of the bath and the stiffness of the harmonic trap vary in time, but in such a way that the average heat vanishes for all times. All branches are swept at a finite rate and, therefore, the corresponding processes are irreversible, not quasi-static. Specifi…
Thermodynamic process at zero-entropy-production (EP) rate has been regarded as a reversible process. A process achieving the Carnot efficiency is also considered as a reversible process. Therefore, the condition, `Carnot efficiency at zero-EP rate' could be regarded as a strong equivalent condition for a reversible process. Here, however, we show that the detailed balance can be broken for a zero-EP rate process and even for a process achieving the Carnot efficiency at zero-EP rate in an example of a quantum-dot model. This clearly demonstrates that `Carnot efficiency at zero-EP rate' or just…
Based on a quantum thermodynamic protocol for shortcut to isothermality that smoothly modify the system-reservoir interaction can significantly speed up an isothermal process while keeping the overall dissipation constant [Phys. Rev. X. 10, 031015 (2020)], we extend the study of optimization performance of Carnot-like heat engines and refrigerators in a straightforward and unified way. We derive the universal optimization efficiency of heat engines and the optimization coefficient of performance of refrigerators under two unified optimization criterions, i.e., chi criterion and omega criterion…
We model a microscopic heat engine as a particle hopping on a one-dimensional lattice in a periodic sawtooth potential, with or without load, assisted by the thermal kicks it gets from alternately placed hot and cold thermal baths. We find analytic expressions for current and rate of heat flow when the engine operates at steady state. Three regions are identified where the model acts either as a heat engine or as a refrigerator or as neither of the two. At quasistatic limit both efficiency of the engine and coefficient of performance of the refrigerator go to that for Carnot engine and Carnot …
In a recent Letter [EPL, 118 (2017) 40003], Polettini and Esposito claimed that it is theoretically possible for a thermodynamic machine to achieve Carnot efficiency at divergent power output through the use of infinitely-fast processes. It appears however that this assertion is misleading as it is not supported by their derivations as demonstrated below. In this Comment, we first show that there is a confusion regarding the notion of optimal efficiency. We then analyze the quantum dot engine described in Ref. [EPL, 118 (2017) 40003] and demonstrate that Carnot efficiency is recovered only for…
Carnot's theorem poses a fundamental limit on the maximum efficiency achievable from an engine that works between two reservoirs at thermal equilibrium. We extend this result to the case of arbitrary nonthermal stationary reservoirs, even with quantum coherence. In order to do this we prove that a single nonthermal reservoir is formally equivalent to multiple equilibrium ones. Finally, we discuss the possibility of realizing an engine that works at unit efficiency by exploiting quantum coherence present in the reservoir.
Classically, the power generated by an ideal thermal machine cannot be larger than the Carnot limit. This profound result is rooted in the second law of thermodynamics. A hot question is whether this bound is still valid for microengines operating far from equilibrium. Here, we demonstrate that a quantum chiral conductor driven by AC voltage can indeed work with efficiencies much larger than the Carnot bound. The system also extracts work from common temperature baths, violating Kelvin-Planck statement. Nonetheless, with the proper definition, entropy production is always positive and the seco…
Since its inception about two centuries ago thermodynamics has sparkled continuous interest and fundamental questions. According to the second law no heat engine can have an efficiency larger than Carnot's efficiency. The latter can be achieved by the Carnot engine, which however ideally operates in infinite time, hence delivers null power. A currently open question is whether the Carnot efficiency can be achieved at finite power. Most of the previous works addressed this question within the Onsager matrix formalism of linear response theory. Here we pursue a different route based on finite-si…
We review a series of experimental studies of the thermodynamics of nonequilibrium processes at the microscale. In particular, in these experiments we studied the fluctuations of the thermodynamic properties of a single optically-trapped microparticle immersed in water and in the presence of external random forces. In equilibrium, the fluctuations of the position of the particle can be described by an effective temperature that can be tuned up to thousands of Kelvins. Isothermal and non-isothermal thermodynamic processes that also involve changes in a control parameter were implemented by cont…
Analog of the Carnot engine for fluctuating diffusivity in living cells
本文基于活细胞中的异质扩散现象，提出涨落扩散率与热力学形式类比，构建了类热机模型，其循环效率形式上等同于卡诺效率且循环中熵总变化为零。
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