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Álvarez CE, Camargo M, Téllez G. One-particle engine with a porous piston. Sci Rep 2022; 12:13896. [PMID: 35974083 PMCID: PMC9381796 DOI: 10.1038/s41598-022-18057-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2022] [Accepted: 08/04/2022] [Indexed: 11/29/2022] Open
Abstract
We propose a variation of the classical Szilard engine that uses a porous piston. Such an engine requires neither information about the position of the particle, nor the removal and subsequent insertion of the piston when resetting the engine to continue doing work by lifting a mass against a gravitational field. Though the engine operates in contact with a single thermal reservoir, the reset mechanism acts as a second reservoir, dissipating energy when a mass that has been lifted by the engine is removed to initiate a new operation cycle.
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Affiliation(s)
- Carlos E Álvarez
- Escuela de Ingeniería, Ciencia y Tecnología, Universidad del Rosario, Bogotá, Colombia.
| | - Manuel Camargo
- FIMEB & CICBA, Universidad Antonio Nariño-Campus Farallones, Cali, Colombia
| | - Gabriel Téllez
- Departamento de Física, Universidad de los Andes, Bogotá, Colombia
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2
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Mamede IN, Harunari PE, Akasaki BAN, Proesmans K, Fiore CE. Obtaining efficient thermal engines from interacting Brownian particles under time-periodic drivings. Phys Rev E 2022; 105:024106. [PMID: 35291114 DOI: 10.1103/physreve.105.024106] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2021] [Accepted: 01/18/2022] [Indexed: 06/14/2023]
Abstract
We introduce an alternative route for obtaining reliable cyclic engines, based on two interacting Brownian particles under time-periodic drivings which can be used as a work-to-work converter or a heat engine. Exact expressions for the thermodynamic fluxes, such as power and heat, are obtained using the framework of stochastic thermodynamic. We then use these exact expression to optimize the driving protocols with respect to output forces, their phase difference. For the work-to-work engine, they are solely expressed in terms of Onsager coefficients and their derivatives, whereas nonlinear effects start to play a role since the particles are at different temperatures. Our results suggest that stronger coupling generally leads to better performance, but careful design is needed to optimize the external forces.
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Affiliation(s)
- Iago N Mamede
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
| | - Pedro E Harunari
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Bruno A N Akasaki
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
| | - Karel Proesmans
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
- Hasselt University, B-3590 Diepenbeek, Belgium
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen, Denmark
| | - C E Fiore
- Instituto de Física da Universidade de São Paulo, 05314-970 São Paulo, Brazil
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3
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Álvarez CE, Afanador N, Téllez G. Work done on a single-particle gas during an adiabatic compression and expansion process. Phys Rev E 2019; 100:042110. [PMID: 31770865 DOI: 10.1103/physreve.100.042110] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2019] [Indexed: 06/10/2023]
Abstract
We compute the average work done by an external agent, driving a piston at constant speed, over a single-particle gas going through an adiabatic compression and expansion process. To do so, we get the analytical expression relating the number of collisions between the piston and the particle with the position of the piston during the process. The ergodicity breaking of the system during the process is identified as the source of its irreversibility. In addition, we observe that by using particular initial distributions for the state of the particle, it is possible to preclude the possibility of a net energy transfer from the agent to the particle during the process.
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Affiliation(s)
- Carlos E Álvarez
- Departamento de Matemáticas Aplicadas y Ciencias de la Computación, Universidad del Rosario, Bogotá, Colombia
| | - Nicolás Afanador
- Departamento de Matemáticas Aplicadas y Ciencias de la Computación, Universidad del Rosario, Bogotá, Colombia
| | - Gabriel Téllez
- Departamento de Física, Universidad de los Andes, Bogotá, Colombia
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4
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Izumida Y, Okuda K. Molecular kinetic analysis of a local equilibrium Carnot cycle. Phys Rev E 2017; 96:012123. [PMID: 29347144 DOI: 10.1103/physreve.96.012123] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2017] [Indexed: 06/07/2023]
Abstract
We identify a velocity distribution function of ideal gas particles that is compatible with the local equilibrium assumption and the fundamental thermodynamic relation satisfying the endoreversibility. We find that this distribution is a Maxwell-Boltzmann distribution with a spatially uniform temperature and a spatially varying local center-of-mass velocity. We construct the local equilibrium Carnot cycle of an ideal gas, based on this distribution, and show that the efficiency of the present cycle is given by the endoreversible Carnot efficiency using the molecular kinetic temperatures of the gas. We also obtain an analytic expression of the efficiency at maximum power of our cycle under a small temperature difference. Our theory is also confirmed by a molecular dynamics simulation.
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Affiliation(s)
- Yuki Izumida
- Department of Complex Systems Science, Graduate School of Information Science, Nagoya University, Nagoya 464-8601, Japan
| | - Koji Okuda
- Division of Physics, Hokkaido University, Sapporo 060-0810, Japan
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5
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Gong Z, Lan Y, Quan HT. Stochastic Thermodynamics of a Particle in a Box. PHYSICAL REVIEW LETTERS 2016; 117:180603. [PMID: 27835006 DOI: 10.1103/physrevlett.117.180603] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2016] [Indexed: 06/06/2023]
Abstract
The piston system (particles in a box) is the simplest paradigmatic model in traditional thermodynamics. However, the recently established framework of stochastic thermodynamics (ST) fails to apply to this model system due to the embedded singularity in the potential. In this Letter, we study the ST of a particle in a box by adopting a novel coordinate transformation technique. Through comparing with the exact solution of a breathing harmonic oscillator, we obtain analytical results of work distribution for an arbitrary protocol in the linear response regime and verify various predictions of the fluctuation-dissipation relation. When applying to the Brownian Szilard engine model, we obtain the optimal protocol λ_{t}=λ_{0}2^{t/τ} for a given sufficiently long total time τ. Our study not only establishes a paradigm for studying ST of a particle in a box but also bridges the long-standing gap in the development of ST.
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Affiliation(s)
- Zongping Gong
- School of Physics, Peking University, Beijing 100871, China
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Yueheng Lan
- Department of Physics, Beijing University of Posts and Telecommunications, Beijing 100876, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - H T Quan
- School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
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Gubbiotti G, Chiuchiù D. Thermodynamics of slow solutions to the gas-piston equations. Phys Rev E 2016; 94:042106. [PMID: 27841498 DOI: 10.1103/physreve.94.042106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2016] [Indexed: 06/06/2023]
Abstract
Despite its historical importance, a perfect gas enclosed by a pistons and in contact with a thermal reservoirs is a system still largely under study. Its thermodynamic properties are not yet well understood when driven under nonequilibrium conditions, and analytic formulas that describe the heat exchanged with the reservoir are rare. In this paper we prove a power series expansions for the heat when both the external force and the reservoir temperature are slowly varying over time but the overall process is not quasistatic. To do so, we use the dynamical equations from [Cerino et al., Phys. Rev. E 91, 032128 (2015)PLEEE81539-375510.1103/PhysRevE.91.032128] and an uncommon application of the regular perturbation technique.
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Affiliation(s)
- G Gubbiotti
- Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre and Sezione INFN di Roma Tre, Rome, Italy
| | - D Chiuchiù
- NiPS Lab, Dipartimento di Fisica e Geologia, Università degli Studi di Perugia, Perugia, Italy
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Proesmans K, Driesen C, Cleuren B, Van den Broeck C. Efficiency of single-particle engines. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:032105. [PMID: 26465424 DOI: 10.1103/physreve.92.032105] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2015] [Indexed: 06/05/2023]
Abstract
We study the efficiency of a single-particle Szilard and Carnot engine. Within a first order correction to the quasistatic limit, the work distribution is found to be Gaussian and the correction factor to average work and efficiency only depends on the piston speed. The stochastic efficiency is studied for both models and the recent findings on efficiency fluctuations are confirmed numerically. Special features are revealed in the zero-temperature limit.
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Affiliation(s)
- Karel Proesmans
- Faculty of Sciences, Hasselt University, B-3590 Diepenbeek, Belgium
| | - Cedric Driesen
- Faculty of Sciences, Hasselt University, B-3590 Diepenbeek, Belgium
| | - Bart Cleuren
- Faculty of Sciences, Hasselt University, B-3590 Diepenbeek, Belgium
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Izumida Y, Okuda K, Roco JMM, Hernández AC. Heat devices in nonlinear irreversible thermodynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:052140. [PMID: 26066152 DOI: 10.1103/physreve.91.052140] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2014] [Indexed: 06/04/2023]
Abstract
We present results obtained by using nonlinear irreversible models for heat devices. In particular, we focus on the global performance characteristics, the maximum efficiency and the efficiency at maximum power regimes for heat engines, and the maximum coefficient of performance (COP) and the COP at maximum cooling power regimes for refrigerators. We analyze the key role played by the interplay between irreversibilities coming from heat leaks and internal dissipations. We also discuss the relationship between these results and those obtained by different models.
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Affiliation(s)
- Y Izumida
- Department of Information Sciences, Ochanomizu University 2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8620, Japan
| | - K Okuda
- Division of Physics, Hokkaido University, Sapporo 060-0810, Japan
| | - J M M Roco
- Departamento de Física Aplicada, and Instituto Universitario de Física Fundamental y Matemáticas (IUFFyM), Universidad de Salamanca, 37008 Salamanca, Spain
| | - A Calvo Hernández
- Departamento de Física Aplicada, and Instituto Universitario de Física Fundamental y Matemáticas (IUFFyM), Universidad de Salamanca, 37008 Salamanca, Spain
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Rana S, Pal PS, Saha A, Jayannavar AM. Single-particle stochastic heat engine. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042146. [PMID: 25375477 DOI: 10.1103/physreve.90.042146] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2014] [Indexed: 06/04/2023]
Abstract
We have performed an extensive analysis of a single-particle stochastic heat engine constructed by manipulating a Brownian particle in a time-dependent harmonic potential. The cycle consists of two isothermal steps at different temperatures and two adiabatic steps similar to that of a Carnot engine. The engine shows qualitative differences in inertial and overdamped regimes. All the thermodynamic quantities, including efficiency, exhibit strong fluctuations in a time periodic steady state. The fluctuations of stochastic efficiency dominate over the mean values even in the quasistatic regime. Interestingly, our system acts as an engine provided the temperature difference between the two reservoirs is greater than a finite critical value which in turn depends on the cycle time and other system parameters. This is supported by our analytical results carried out in the quasistatic regime. Our system works more reliably as an engine for large cycle times. By studying various model systems, we observe that the operational characteristics are model dependent. Our results clearly rule out any universal relation between efficiency at maximum power and temperature of the baths. We have also verified fluctuation relations for heat engines in time periodic steady state.
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Affiliation(s)
- Shubhashis Rana
- Institute of Physics, Sachivalaya Marg, Bhubaneswar-751005, India
| | - P S Pal
- Institute of Physics, Sachivalaya Marg, Bhubaneswar-751005, India
| | - Arnab Saha
- Institut för Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - A M Jayannavar
- Institute of Physics, Sachivalaya Marg, Bhubaneswar-751005, India
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Leonard T, Lander B, Seifert U, Speck T. Stochastic thermodynamics of fluctuating density fields: Non-equilibrium free energy differences under coarse-graining. J Chem Phys 2013; 139:204109. [DOI: 10.1063/1.4833136] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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