Carnot’s cycle for small systems: Irreversibility and cost of operations

Sekimoto, Ken; Takagi, Fumiko; Hondou, Tsuyoshi

doi:10.1103/physreve.62.7759

Cited by 76 publications

(104 citation statements)

References 21 publications

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“…The PDF is continuous and thus the equilibrium distribution before and after the adiabatic branches must be the same. This is possible only when the sudden changes of temperature during the adiabatic branches are suitably balanced by the discontinuities of the driving [59,67].…”

Section: Useful and Dud Heat Enginesmentioning

confidence: 99%

Efficiency at and near maximum power of low-dissipation heat engines

Holubec

Ryabov

2015

Phys. Rev. E

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A new universality in optimization of trade-off between power and efficiency for low-dissipation Carnot cycles is presented. It is shown that any trade-off measure expressible in terms of efficiency and the ratio of power to its maximum value can be optimized independently of most details of the dynamics and of the coupling to thermal reservoirs. The result is demonstrated on two specific trade-off measures. The first one is designed for finding optimal efficiency for a given output power and clearly reveals diseconomy of engines working at maximum power. As the second example we derive universal lower and upper bounds on the efficiency at maximum trade-off given by the product of power and efficiency. The results are illustrated on a model of a diffusion-based heat engine. Such engines operate in the low-dissipation regime given that the used driving minimizes the work dissipated during the isothermal branches. The peculiarities of the corresponding optimization procedure are reviewed and thoroughly discussed.

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Section: Useful and Dud Heat Enginesmentioning

confidence: 99%

Efficiency at and near maximum power of low-dissipation heat engines

Holubec

Ryabov

2015

Phys. Rev. E

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“…Under these conditions the entropy production vanishes and hence the system works in reversible mode [36].…”

Section: Overdamped Dynamicsmentioning

confidence: 99%

Operational characteristics of single-particle heat engines and refrigerators with time-asymmetric protocol

Pal

Saha

Jayannavar

2016

Int. J. Mod. Phys. B

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We have studied the single particle heat engine and refrigerator driven by time asymmetric protocol of finite duration. Our system consists of a particle in a harmonic trap with time-periodic strength that drives the particle cyclically between two baths. Each cycle consists of two isothermal steps at different temperatures and two adiabatic steps connecting them. The system works in irreversible mode of operation even in the quasistatic regime. This is indicated by finite entropy production even in the large cycle time limit. Consequently, Carnot efficiency for heat engine or Carnot Co-efficient of performance (COP) for refrigerators are not achievable. We further analysed the phase diagram of heat engines and refrigerators. They are sensitive to time-asymmetry of the protocol. Phase diagram shows several interesting features, often counterintuitive. The distribution of stochastic efficiency and COP is broad and exhibits power law tails.In recent years a lot of interest has been generated in the study of stochastic single particle heat engines and refrigerators [1,2,3,4,5,6,7,8,9,10,11]. Engines at nanoscale are ubiquitous in biology [12,13,14] and become increasingly pertinent synthetically. With the progress of technology micrometer sized stochastic heat engines have been realised experimentally [15,16,17,18]. At these length scales thermal fluctuation plays a pivotal role in determining the performance characteristics of the system. Typical energy transformations (work and heat) in these systems are of the order of k B T , where T is the temperature of the surrounding reservoir.Therefore taking account of thermal fluctuations is an absolute necessity to achieve engineering capabilities in designing such small scale devices [19].The apt theory for the thermodynamics of small scale devices comes under the frame work of stochastic thermodynamics where the macroscopic thermodynamic variables (e.g. work, heat, total entropy, internal energy etc.) are defined over a single trajectory and thereby differs stochastically from one measurement to another [20,21,22,23,24,25,26,27]. Besides validating macro thermodynamics after averaging over all possible trajectories, the new frame work offers first law like equality defined over a single trajectory and fluctuation theorems [28,29,30,31,32,33], a set of equalities between stochastically varying thermodynamic variables that put rigorous constraints to their distributions.Using stochastic thermodynamics microscopic heat engines and refrigerators have been explored. Extensive studies including both quasistatic and nonquasistatic regime have been done on systems consisting of a harmonically trapped Brownian particle driven periodically (with period τ ) by the time dependent strength of the confining potential within two thermal reservers having different temperatures T h and T l where T h > T l [10,11]. The protocol studied in [10,11] consists of two isotherms having equal length along time axis (that is why the protocol can be termed as time-symmetric) and two adia...

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“…We would like to emphasize that only for T h T l = 2, q equals Carnot limit. This is an interesting observation [59]. It is important to note that the adiabatic jumps, being instantaneous, the probability distribution remains unchanged during this process.…”

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confidence: 99%

Anomalous Brownian refrigerator

Rana

Pal

Saha

et al. 2016

Physica A: Statistical Mechanics and its Applications

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We present a detailed study of a Brownian particle driven by Carnot-type refrigerating protocol operating between two thermal baths. Both the underdamped as well as the overdamped limits are investigated. The particle is in a harmonic potential with time-periodic strength that drives the system cyclically between the baths. Each cycle consists of two isothermal steps at different temperatures and two adiabatic steps connecting them. Besides working as a stochastic refrigerator, it is shown analytically that in the quasistatic regime the system can also act as stochastic heater, depending on the bath temperatures. Interestingly, in non-quasistatic regime, our system can even work as a stochastic heat engine for certain range of cycle time and bath temperatures. We show that the operation of this engine is not reliable. The fluctuations of stochastic efficiency/coefficient of performance (COP) dominate their mean values. Their distributions show power law tails, however the exponents are not universal. Our study reveals that microscopic machines are not the microscopic equivalent of the macroscopic machines that we come across in our daily life. We find that there is no one to one correspondence between the performance of our system under engine protocol and its reverse.

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Carnot’s cycle for small systems: Irreversibility and cost of operations

Cited by 76 publications

References 21 publications

Efficiency at and near maximum power of low-dissipation heat engines

Efficiency at and near maximum power of low-dissipation heat engines

Operational characteristics of single-particle heat engines and refrigerators with time-asymmetric protocol

Anomalous Brownian refrigerator

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