Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session V15: Focus Session: Nonequilibrium Thermodynamics of Small Systems |
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Sponsoring Units: GSNP DBP Chair: R. Dean Astumian, University of Maine Room: Colorado Convention Center Korbel 4E |
Thursday, March 8, 2007 11:15AM - 11:51AM |
V15.00001: The nonequilibrium thermodynamics of small systems Invited Speaker: Nonequilibrium behavior is widespread and rich in nature. Yet our understanding of the fundamental principles underlying nonequilibrium behavior is still poor as shown by the fact that non-equilibrium theories tend to be ad-hoc and specific (1). Recently there has been a lot of interest in applying single-molecule techniques to scrutinize nonequilibrium theories (2). The use of new micromanipulation tools in the exploration of the behavior of tiny objects (such as biomolecules and motors) embedded in a thermal environment opens the possibility to investigate how these systems exchange energy with their environment. The study of such questions, nowadays referred to as ``Nonequilibrium thermodynamics of small systems,'' is becoming quite popular among statistical physicists who recognize there new aspects of thermodynamics where large Brownian fluctuations are of pivotal importance as compared to fluctuations in macroscopic (or large) systems (3). Nonequilibrium small systems are characterized by large deviations in work/heat distributions that satisfy some relations called fluctuation theorems. In this talk I will discuss single-molecule experiments where some of these fluctuation theorems have been tested (4). \newline \newline REFERENCES: \newline (1) F. Ritort, Nonequilibrium fluctuations in small sytems: From physics to biology, To be published in Advances in Chemical Physics, volume 137; \newline (2) F. Ritort, Single molecule experiments in biological physics: methods and applications, Journal of Physics C (Condensed Matter),18 (2006) R531-R583; \newline (3) C. Bustamante, J. Liphardt and F. Ritort, The nonequilibrium thermodynamics of small systems, Physics Today,58 (2005) 43-48; \newline (4) D. Collin, F. Ritort, C. Jarzynski, S. B. Smith, I. Tinoco Jr and C. Bustamante, Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies, Nature, 437 (2005) 231-234. [Preview Abstract] |
Thursday, March 8, 2007 11:51AM - 12:03PM |
V15.00002: Activation barrier scaling and crossover for noise-induced switching in a micromechanical parametric oscillator Corey Stambaugh, Ho Bun Chan We explore fluctuation-induced switching in a parametrically-driven micromechanical torsional oscillator, a system far from thermal equilibrium. Under sufficiently strong parametric modulation of the spring constant, the oscillator possesses one, two or three stable attractors depending on the modulation frequency. Near the bifurcation points where the number of attractors changes, the activation barrier for switching out of a stable state is predicted to display universal, system-independent scaling relationships. We induce the oscillator to switch between the coexisting states by injecting noise in the excitation. By measuring the rate of random transitions as a function of noise intensity, we deduce the activation barrier as a function of frequency. Near both bifurcation points, the activation barriers are found to depend on frequency detuning with critical exponent of 2, consistent with the predicted universal scaling in parametrically driven systems. Away from the immediate vicinity of the bifurcation point, universal scaling relationships for the activation barrier no longer hold. At large detuning, we observe a crossover to a different power law dependence with an exponent that is specific to our device. [Preview Abstract] |
Thursday, March 8, 2007 12:03PM - 12:15PM |
V15.00003: Scaling crossovers in activated escape of nonequilibrium systems: a resonantly driven oscillator Oleg Kogan, Ira Schwartz, Mark Dykman The rate of metastable decay in nonequilibrium systems is expected to display scaling behavior: i.e., the logarithm of the decay rate should scale as a power of the distance to a bifurcation point where themetastable state disappears. Recently such behavior was observed and some of the earlier predicted exponents were found in experiments on several types of systems described by a model of a modulated oscillator. Here we establish the range where different scaling behavior is displayed and show how the crossover between different types of scaling occurs. The analysis is done for a nonlinear oscillator with two coexisting stable states of forced vibrations. We map out the entire parameter range. We find the regions where the scaling exponents are 1 or 3/2, depending on the damping. We also uncover new scaling behavior which extends, numerically, beyond the close vicinity of the bifurcation point. The results of the numerical calculations based on the instanton method are compared with the results of Monte Carlo simulations. [Preview Abstract] |
Thursday, March 8, 2007 12:15PM - 12:27PM |
V15.00004: Spontaneous symmetry breaking in parametrically driven atomic trap and measurement of dynamic critical exponents Wonho Jhe, Myoung-Sun Heo, Yonghee Kim, Kiwhan Kim, Heung-Ryoul Noh While critical phenomena in equilibrium systems has been well established both in theory and in experiment, experimental studies in~ non-equilibrium or far-from-equilibrium systems still lack of quantitative investigation and remain as challenging subjects. Here we report on the use of laser cooled and trapped atoms can be a good candidate for such study since one can easily control its temperature and numbers. By parametrically modulating the magneto-optical trap potential we have observed several interesting phenomena such as dynamic double well, Hopf bifurcation and spontaneous symmetry-breaking (SSB). Particularly SSB is identified as the mean-field system exhibiting the Ising-like phase transition. We measured critical exponents relevant to this phase transition, with respect to the control parameter, the size of the system or the total number of atoms. We also have observed the occurrence of SSB as the temperature is changed by illuminating a resonant laser light. [Preview Abstract] |
Thursday, March 8, 2007 12:27PM - 12:39PM |
V15.00005: Equilibrium theory for a particle pulled by a moving optical trap Raymond Dean Astumian The viscous drag on a colloidal particle pulled through solution by an optical trap is large enough that on experimentally relavant time scales the mechanical force exerted by the trap is equal and opposite the viscous drag force. The rapid mechanical equilibritation allows the system to be modeled using equilibrium theory where the effects of the energy dissipation ({\em thermodynamic} disequilibrium) show up only in the coordinate transformations that map the system from the laboratory frame of reference, relative to which the particle is moving, to a frame of reference in which the particle is, on average, stationary and on which the stochastic dynamics is governed by a canonical equilibrium distribution function. The simple equations in the stationary frame can be analyzed using the Onsager-Machlup theory for stochastic systems and provide generalizations of equilibrium and near equilibrium concepts such as detailed balance and fluctuation-dissipation relations applicable to a wide range of systems including molecular motors, pumps, and other nano-scale machines. [Preview Abstract] |
Thursday, March 8, 2007 12:39PM - 12:51PM |
V15.00006: Energy and efficiency optimization of a Brownian heat engine Mulugeta Bekele, Yeneneh Yalew A simple Brownian heat engine is modeled as a Brownian particle moving in an external sawtooth potential (with or without) load assisted by the thermal kick it gets from alternately placed hot and cold heat reservoirs along its path. We get closed form expression for its current in terms of the parameters characterizing the model. After analyzing the way it consumes energy to do useful work, we also get closed form expressions for its efficiency as well as for its coefficient of performance when the engine performs as a refrigerator. Recently suggested optimization criteria enables us to exhaustively explore and compare the different operating conditions of the engine. [Preview Abstract] |
Thursday, March 8, 2007 12:51PM - 1:03PM |
V15.00007: Relationships involving spatial transitions for Brownian particles within a potential-well. Ross Brody Using an optical tweezer apparatus we have trapped single latex spheres and analyzed their Brownian motion within a potential well. By considering transitions from various initial and final positions within the well, we experimentally show that the ratio of conditional probabilities, $P(x_f,t+\Delta t|x_i,t)/P(x_i,t+\Delta t|x_f,t)$, is independent of $\Delta t$. We also show the instanton times corresponding to last-touch-first-touch (LTFT) trajectories obey the equality, LTFT($x_i\rightarrow x_f$)=LTFT($x_f\rightarrow x_i$), shown by Bier et al. [Phys. Rev. E \bf{59}\rm, 6422 (1999)]. [Preview Abstract] |
Thursday, March 8, 2007 1:03PM - 1:15PM |
V15.00008: Analytical calculation of Jarzynski free-energy estimator bias Matteo Palassini, Nikos Skantzos, Felix Ritort The Jarzynski equality connects the free-energy difference DF between two equilibrium states A and B of a system to the work done on the system in a non-equilibrium process that takes it from A to B, averaged exponentially over all possible realizations of the process. This provides an estimator for DF given N non-equilibrium experiments, which has been applied in a variety of contexts. Because of the exponential averaging, the Jarzynski estimator suffers a statistical bias for finite N, which can be substantial. Computing this bias is important for estimating correctly the free-energy, and is a notoriously difficult problem for which only results in the large-N limit are known. We propose an analytical method to estimate the bias and test it in the case of a Gaussian work distribution, for which it provides satisfactory estimates both in the large N and small N regimes. Finally, we discuss the applicability of these results to experimental studies on single biomolecules. [Preview Abstract] |
Thursday, March 8, 2007 1:15PM - 1:27PM |
V15.00009: Exact equality between dissipation and irreversibility Ryoichi Kawai, Juan M. R. Parrondo, Christian Van den Broeck We show, through a reformulation of the Crooks theorem and the Jarzynski equality, that the average dissipation for a system perturbed to go from one equilibrium state to another one, is exactly given by $\langle W \rangle_{diss} = \langle W \rangle -\Delta F =kT D(\rho\|\widetilde{\rho})= kT \langle \ln (\rho/\widetilde{\rho})\rangle$, where $\rho$ and $\widetilde{\rho}$ are the phase space density of the system measured at the same but otherwise arbitrary intermediate point in time, for the forward and backward process. $D(\rho\|\widetilde{\rho})$ is the relative entropy of $\rho$ versus $\widetilde{\rho}$. [Preview Abstract] |
Thursday, March 8, 2007 1:27PM - 1:39PM |
V15.00010: Free Energy Surface Reconstruction Using Jarzynski's Equality Ching-Hwa Kiang, Nolan Harris Atomic force microscope was used to manipulate and unfold individual molecules of the muscle protein titin. We reconstructed the free energy surface of stretching and unfolding of titin I27 domain using Jarzynski's equality. An exact formula that relates the nonequilibrium work fluctuations to the molecular free energy was used for the reconstruction. From the free energy surface, the unfolding free energy barrier, i.e. the activation energy, was directly obtained from experimental data for the first time. [Preview Abstract] |
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