Equalities and Inequalities: Irreversibility and the Second Law of Thermodynamics at the Nanoscale

Jarzynski, Christopher

doi:10.1007/978-3-0348-0359-5_4

Cited by 162 publications

(278 citation statements)

References 66 publications

(76 reference statements)

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“…A consequence of (2) is a version of the second law ∆S sys + β δQ ≥ 0 where S sys = − ∑ i p i log p i is the system entropy and ∆S sys is its change from the initial to the final state. Stochastic thermodynamics is covered by several excellent reviews to which I direct the reader for further information and pointers to the literature [3][4][5][6][7]. A limitation of stochastic thermodynamics in the standard formulation is that it neglects the energy stored in the coupling between the system and the bath.…”

Section: Introductionmentioning

confidence: 99%

On Work and Heat in Time-Dependent Strong Coupling

Aurell

2017

Entropy

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This paper revisits the classical problem of representing a thermal bath interacting with a system as a large collection of harmonic oscillators initially in thermal equilibrium. As is well known, the system then obeys an equation, which in the bulk and in the suitable limit tends to the Kramers-Langevin equation of physical kinetics. I consider time-dependent system-bath coupling and show that this leads to an additional harmonic force acting on the system. When the coupling is switched on and switched off rapidly, the force has delta-function support at the initial and final time. I further show that the work and heat functionals as recently defined in stochastic thermodynamics at strong coupling contain additional terms depending on the time derivative of the system-bath coupling. I discuss these terms and show that while they can be very large if the system-bath coupling changes quickly, they only give a finite contribution to the work that enters in Jarzynski's equality. I also discuss that these corrections to standard work and heat functionals provide an explanation for non-standard terms in the change of the von Neumann entropy of a quantum bath interacting with a quantum system found in an earlier contribution (Aurell and Eichhorn, 2015).

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Section: Introductionmentioning

confidence: 99%

On Work and Heat in Time-Dependent Strong Coupling

Aurell

2017

Entropy

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“…While since the seminal works of Boltzmann, the main efforts of those working in the foundations of statistical mechanics were directed to reconcile the Minus-First Law with the time-reversal symmetric microscopic dynamics, recent developments in the theory of fluctuation relations have brought new and deep insights into the microscopic foundations of the Second Law. As we shall see below, fluctuation theorems highlight in a most clear way the fascinating fact that the Second Law is deeply rooted in the time-reversal symmetric nature of the laws of microscopic dynamics [6,7].…”

Section: Introductionmentioning

confidence: 99%

“…Fluctuation theorems exist for classical dynamics, stochastic dynamics, and for quantum dynamics; for transiently driven systems, as well as for non-equilibrium steady states; for systems prepared in canonical, micro-canonical, grand-canonical ensembles, and even for systems initially in contact with "finite heat baths" [9]; they can refer to different quantities like work (different kinds), entropy production, exchanged heat, exchanged charge, and even information, depending on different set-ups. All these developments including discussions of the experimental applications of fluctuation theorems have been summarized in a number of reviews [6,7,10,11].…”

Section: Introductionmentioning

confidence: 99%

Fluctuation, Dissipation and the Arrow of Time

Campisi

Hänggi

2011

Entropy

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“…The original description of classical heat engines by Sadi Carnot in 1824 has largely shaped our understanding of work and heat exchange during macroscopic thermodynamic processes 1 . Equipped with our present-day ability to design and control mechanical devices at micro-and nanometre length scales, we are now in a position to explore the limitations of classical thermodynamics, arising on scales for which thermal fluctuations are important [2][3][4][5] . Here we demonstrate the experimental realization of a microscopic heat engine, comprising a single colloidal particle subject to a time-dependent optical laser trap.…”

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confidence: 99%

“…3a). Finally, we also investigated the efficiency of our engine, which is given by the ratio between extracted work and the average absorbed heat cJh at the hot temperature, that is 17 = wfiih· Using the first law of thermodynamics it follows that the heat absorbed during the expansion at Tb is q h 4 = w 3 ... 4 To perform step {3} -7 {4} quasistatically the system has to relax into equilibrium after tile sudden temperature increase (2} -7 (3}. This relaxation is connected to an additional average heat flow cJz-+3 = -Llii2-+3 = -keTb(l -Tb/Tc).…”

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confidence: 99%

Realization of a micrometre-sized stochastic heat engine

2011

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The conversion of energy into mechanical work is essential for almost any industrial process. The original description of classical heat engines by Sadi Carnot in 1824 has largely shaped our understanding of work and heat exchange during macroscopic thermodynamic processes 1 . Equipped with our present-day ability to design and control mechanical devices at micro-and nanometre length scales, we are now in a position to explore the limitations of classical thermodynamics, arising on scales for which thermal fluctuations are important 2-5 . Here we demonstrate the experimental realization of a microscopic heat engine, comprising a single colloidal particle subject to a time-dependent optical laser trap. The work associated with the system is a fluctuating quantity, and depends strongly on the cycle duration time, τ, which in turn determines the efficiency of our heat engine. Our experiments offer a rare insight into the conversion of thermal to mechanical energy on a microscopic level, and pave the way for the design of future micromechanical machines.Macroscopic heat engines operating periodically between two heat baths are described well by the laws of thermodynamics, owing to the large number of internal degrees of freedom, which render fluctuations negligible. In contrast, fluctuations become visible when the typical energy scales of engines are reduced by more than twenty orders of magnitude, down to values around k B T . This regime can be achieved when the typical system dimensions are scaled down from metres to micrometres 2 . Such conditions are typically met for biomolecules 6,7 and other microelectromechanical systems (MEMS; refs 8-10) that can perform translational or rotational motion as a result of chemical reactions and electrical fields. Also, several types of Brownian motor have been discussed that are able to extract useful work by rectification of thermal noise [11][12][13] . Despite its conceptual simplicity, no attempt has been made to realize a microscopic heat engine that extracts energy by cyclically working between two heat baths in a regime where fluctuations dominate.Here we present an experimental realization of a Stirling engine, where a single Brownian particle is subjected to a time-dependent optical trap and periodically coupled to different heat baths 14 . The particle and the trapping potential replace the working gas and the piston of its macroscopic counterpart. As for conventional heat engines where the periodic coupling of the working gas to a cold and a hot heat bath changes volume and pressure inside a piston, the fluctuations of a colloidal particle subjected to an external optical potential vary on changing the temperature of the solvent.As a Brownian particle we used a single melamine bead of diameter 2.94 μm suspended in water and confined in a vitreous sample cell 4 μm in height. Using a highly focused infrared laser beam we exerted a parabolic trapping potential U (R,k) = (1/2)k(t )R 2 on the particle, where R is its radial distance from the trapping centre and k(t ), ...

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Equalities and Inequalities: Irreversibility and the Second Law of Thermodynamics at the Nanoscale

Cited by 162 publications

References 66 publications

On Work and Heat in Time-Dependent Strong Coupling

On Work and Heat in Time-Dependent Strong Coupling

Fluctuation, Dissipation and the Arrow of Time

Realization of a micrometre-sized stochastic heat engine

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