The Nonequilibrium Thermodynamics of Small Systems

Bustamante, Carlos; Liphardt, Jan; Ritort, Fèlix

doi:10.1063/1.2012462

Cited by 680 publications

(762 citation statements)

References 30 publications

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“…1 -2012/6/7 -19:43 -page 2 2 ten years has shown that FRs hold for a great variety of systems thus featuring one of the rare statistical physical principles that is valid even very far from equilibrium: see summaries in [13,14,15,16,17,18] for stochastic processes, [19,20,21,22,23,24] for deterministic dynamics and [25,26] for quantum systems. Many of these relations have meanwhile been verified in experiments on small systems, i.e., systems on molecular scales featuring only a limited number of relevant degrees of freedom [27,28,29,30,31,32], cf. the Chapters by Ciliberto et al, Alemany et al, and Sagawa and Ueda.…”

Section: Introductionmentioning

confidence: 99%

Anomalous Fluctuation Relations

Klages

Chechkin

Dieterich

2013

Nonequilibrium Statistical Physics of Small Systems

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Abstract. We study Fluctuation Relations (FRs) for dynamics that are anomalous, in the sense that the diffusive properties strongly deviate from the ones of standard Brownian motion. We first briefly review the concept of transient work FRs for stochastic dynamics modeled by the ordinary Langevin equation. We then introduce three generic types of dynamics generating anomalous diffusion: Lévy flights, long-time correlated Gaussian stochastic processes and time-fractional kinetics. By combining Langevin and kinetic approaches we calculate the work probability distributions in the simple nonequilibrium situation of a particle subject to a constant force. This allows us to check the transient FR for anomalous dynamics. We find a new form of FRs, which is intimately related to the validity of fluctuation-dissipation relations. Analogous results are obtained for a particle in a harmonic potential dragged by a constant force. We argue that these findings are important for understanding fluctuations in experimentally accessible systems. As an example, we discuss the anomalous dynamics of biological cell migration both in equilibrium and in nonequilibrium under chemical gradients.

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Section: Introductionmentioning

confidence: 99%

Anomalous Fluctuation Relations

Klages

Chechkin

Dieterich

2013

Nonequilibrium Statistical Physics of Small Systems

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“…In this paper, we present a brief introduction to stochastic thermodynamics. We refer to the literature for more advanced reviews [5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Ensemble and trajectory thermodynamics: A brief introduction

Broeck

Esposito

2015

Physica A: Statistical Mechanics and its Applications

338

448

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h i g h l i g h t s• We review stochastic thermodynamics at the ensemble level.• We formulate first and second laws at the trajectory level.• The stochastic entropy production is the log-ratio of trajectory probabilities.• We establish the relation between the stochastic grand potential, work and entropy production.• We derive detailed and integral fluctuation theorems. a r t i c l e i n f o b s t r a c tWe revisit stochastic thermodynamics for a system with discrete energy states in contact with a heat and particle reservoir.

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“…fluctuate 9,10 . In fact, stochastic violations of the second law have been observed 11,12 ; nonetheless, the second law still holds, on average, if the initial state is in thermal equilibrium: F −W ≤ 0, where F is the free-energy difference between states, W the work done on the system and · the ensemble average.…”

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confidence: 99%

Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality

et al. 2010

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In 1929, Leó Szilárd invented a feedback protocol 1 in which a hypothetical intelligence-dubbed Maxwell's demon-pumps heat from an isothermal environment and transforms it into work. After a long-lasting and intense controversy it was finally clarified that the demon's role does not contradict the second law of thermodynamics, implying that we can, in principle, convert information to free energy 2-6 . An experimental demonstration of this information-to-energy conversion, however, has been elusive. Here we demonstrate that a non-equilibrium feedback manipulation of a Brownian particle on the basis of information about its location achieves a Szilárd-type information-to-energy conversion. Using realtime feedback control, the particle is made to climb up a spiral-staircase-like potential exerted by an electric field and gains free energy larger than the amount of work done on it. This enables us to verify the generalized Jarzynski equality 7 , and suggests a new fundamental principle of an 'information-to-heat engine' that converts information into energy by feedback control.To illustrate the basic idea of our feedback protocol, let us consider a microscopic particle on a spiral-staircase-like potential ( Fig. 1). We set the height of each step comparable to the thermal energy k B T , where k B is the Boltzmann constant and T is temperature. Subjected to thermal fluctuations, the particle jumps between steps stochastically. Although the particle sometimes jumps to an upper step, downward jumps along the gradient are more frequent than upward jumps. In this manner, on average, the particle falls down the stairs unless it is externally pushed up (Fig. 1a). Now, let us consider the following feedback control: We measure the particle's position at regular intervals, and if an upward jump is observed we place a block behind the particle to prevent subsequent downward jumps (Fig. 1b). If this procedure is repeated, the particle is expected to climb up the stairs. Note that, in the ideal case, energy to place the block can be negligible; this implies that the particle can obtain free energy without any direct energy injection. In such a case, what drives the particle to climb up the stairs? This apparent contradiction to the second law of thermodynamics, epitomized by Maxwell's demon, inspired many physicists to generalize the principles of thermodynamics 1,5,6 . It is now understood that the particle is driven by the 'information' gained by the measurement of the particle's location 5,8 .In microscopic systems, thermodynamic quantities such as work, heat and internal energy do not remain constant but particle on a spiral-staircase-like potential with a step height comparable to k B T. The particle stochastically jumps between steps owing to thermal fluctuations. As the downward jumps along the gradient are more frequent than the upward ones, the particle falls down the stairs, on average. b, Feedback control. When an upward jump is observed, a block is placed behind the particle to prevent downward jumps. By repeating ...

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The Nonequilibrium Thermodynamics of Small Systems

Cited by 680 publications

References 30 publications

Anomalous Fluctuation Relations

Anomalous Fluctuation Relations

Ensemble and trajectory thermodynamics: A brief introduction

Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality

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