Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session D16: Systems Far from Equilibrium |
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Sponsoring Units: GSNP Chair: Beate Schmittmann, Iowa State University Room: 401 |
Monday, March 3, 2014 2:30PM - 2:42PM |
D16.00001: ABSTRACT WITHDRAWN |
Monday, March 3, 2014 2:42PM - 2:54PM |
D16.00002: Driven Langevin systems: fluctuation theorems and faithful dynamics David Sivak, John Chodera, Gavin Crooks Stochastic differential equations of motion (e.g., Langevin dynamics) provide a popular framework for simulating molecular systems. Any computational algorithm must discretize these equations, yet the resulting finite time step integration schemes suffer from several practical shortcomings. We show how any finite time step Langevin integrator can be thought of as a driven, nonequilibrium physical process. Amended by an appropriate work-like quantity (the shadow work), nonequilibrium fluctuation theorems can characterize or correct for the errors introduced by the use of finite time steps. We also quantify, for the first time, the magnitude of deviations between the sampled stationary distribution and the desired equilibrium distribution for equilibrium Langevin simulations of solvated systems of varying size. We further show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts. [Preview Abstract] |
Monday, March 3, 2014 2:54PM - 3:06PM |
D16.00003: Establishing a Nonequilibrium Fluctuation-Dissipation Theorem Through Simultaneous Measurement of the Power Spectral Density and Transfer Function of Driven Systems Alexander Trevelyan, Eric Corwin We explore the response of a model statistical system to strong, non-linear perturbations to its state variables. Specifically, we work with a tunable model of Johnson-Nyquist noise, designed to permit a driving of both the drift and diffusion terms in the associated White Noise Langevin Equation. We achieve a simultaneous measurement of both sides of the Fluctuation Dissipation Theorem (FDT) by driving the circuit with digitally generated white noise and measuring the output. This allows us to calculate a frequency-dependent effective temperature for the driven system, which for an equilibrium system should be set by the energy scale of the input white noise. Comparison of the two sides of FDT--the circuit's transfer function and the power spectral density of the voltage fluctuations--across frequency-space proves non-trivial, and methods are discussed for achieving the most reliable estimate. After comparing the response for a series of functional signals, we find that FDT, measured in this simultaneous fashion, remains intact even while the system is being actively driven out of equilibrium. [Preview Abstract] |
Monday, March 3, 2014 3:06PM - 3:18PM |
D16.00004: Quantum diffusion and entropy production: An exactly solvable model Wim Magnus, Kwinten Nelissen An exact, analytical solution of a simple, quantum mechanical model describing diffusion currents flowing between two fermion reservoirs is presented. The quantum fluctuations characterizing the transient diffusion current and entropy production are explicitly shown, whereas the long-time behavior of the fermion densities is determined by a power law. The interaction Hamiltonian defining the coupling between the reservoirs is related to fermions hopping between real space sites. [Preview Abstract] |
Monday, March 3, 2014 3:18PM - 3:30PM |
D16.00005: Quantum entropy production in phase space Sebastian Deffner A fluctuation theorem for the nonequilibrium entropy production in quantum phase space is derived, which enables the consistent thermodynamic description of arbitrary quantum systems, open and closed. The new treatment naturally generalizes classical results to the quantum domain. As an illustration the harmonic oscillator dragged through a thermal bath is solved numerically. Finally, the significance of the new approach is discussed in detail, and the phase space treatment is opposed to the two time energy measurement approach.\\[4pt] Ref.: S. Deffner, EPL (Europhysics Lett.) \textbf{103}, 30001 (2013) [Preview Abstract] |
Monday, March 3, 2014 3:30PM - 3:42PM |
D16.00006: Prediction of HR/BP response to the spontaneous breathing trial by fluctuation dissipation theory Man Chen We applied the non-equilibrium fluctuation dissipation theorem to predict how critically-ill patients respond to treatment, based on both heart rate data and blood pressure data collected by standard hospital monitoring devices. The non-equilibrium fluctuation dissipation theorem relates the response of a system to a perturbation to the fluctuations in the stationary state of the system. It is shown that the response of patients to a standard procedure performed on patients, the spontaneous breathing trial (SBT), can be predicted by the non-equilibrium fluctuation dissipation approach. We classify patients into different groups according to the patients' characteristics. For each patient group, we extend the fluctuation dissipation theorem to predict interactions between blood pressure and beat-to-beat dynamics of heart rate in response to a perturbation (SBT), We also extract the form of the perturbation function directly from the physiological data, which may help to reduce the prediction error. We note this method is not limited to the analysis of the heart rate dynamics, but also can be applied to analyze the response of other physiological signals to other clinical interventions. [Preview Abstract] |
Monday, March 3, 2014 3:42PM - 3:54PM |
D16.00007: Calculating free energy profiles and identifying the underlying dynamics in systems with memory effects from bi-directional pulling processes Jiong Zhang, Ioan Kosztin A proper description of the effective dynamics of a biomolecular system along a relevant reaction coordinate (RC) requires not only the determination of the corresponding free energy profile (potential of mean force or PMF) but also the correct identification of the underlying stochastic model. While there exist several methods for determining the PMF from fast non-equilibrium pulling processes, for simplicity reasons, it is generally assumed that the dynamics along the RC is that of a simple overdamped Brownian particle with known diffusion coefficient. However, in general, the dynamics along the RC is non-Markovian and can be modeled with a generalized Langevin equation characterized by a friction memory kernel. Here we propose and demonstrate a method that permits the simultaneous determination of both PMF and friction memory kernel from fast bi-directional (forward and time-reversed) pulling processes. As a result, one can identify whether the diffusion along the RC is normal or anomalous (e.g., subdiffusion). The proposed method provides a novel approach for identifying and characterizing the underlying dynamics along a RC of a biomolecular system studied by either single-molecule force microscopy or steered molecular dynamics simulations. [Preview Abstract] |
Monday, March 3, 2014 3:54PM - 4:06PM |
D16.00008: High-precision work distributions for extreme non-equilibrium processes in large systems Alexander Hartmann The distributions of work for strongly non-equilibrium processes are studied using a very general form of a large-deviation approach, which allows one to study distributions down to extremely small probabilities of almost arbitrary quantities of interest for equilibrium, non-equilibrium stationary and even non-stationary processes. The method is applied to varying quickly the external field in a wide range $B=3\ \leftrightarrow 0$ for critical ($T=2.269$) two-dimensional Ising system of size $L\times L=128\times 128$. To obtain free energy differences from the work distributions, they must be studied in ranges where the probabilities are as small as $10^{-240}$, which is not possible using direct simulation approaches. By comparison with the exact free energies, one sees that the present approach allows one to obtain the free energy with a very high relative precision of $10^{-4}$. This works well also for non-zero field, i.e., for a case where standard umbrella-sampling methods seem to be not so efficient to calculate free energies. Furthermore, for the present case it is verified that the resulting distributions of work fulfill Crooks theorem with high precision. Finally, the free energy for the Ising magnet as a function of the field strength is obtained. [Preview Abstract] |
Monday, March 3, 2014 4:06PM - 4:18PM |
D16.00009: Chirality, Causality, and Fluctuation-Dissipation Theorems in Nonequilibrium Steady States Dima Feldman, Chenjie Wang Edges of some quantum Hall liquids and a number of other systems exhibit chiral transport: excitations can propagate in one direction only, e.g., clockwise. We derive a family of fluctuation-dissipation relations in nonequilibrium steady states of such chiral systems. The theorems connect nonlinear response with fluctuations far from thermal equilibrium and hold only in case of chiral transport. They can be used to test the chiral or nonchiral character of the system.\\[4pt] [1] C. Wang and D. E. Feldman, Phys. Rev. Lett. 110, 030602 (2013) [Preview Abstract] |
Monday, March 3, 2014 4:18PM - 4:30PM |
D16.00010: Inconsistencies in steady state thermodynamics Ronald Dickman, Ricardo Motai We address the issue of extending thermodynamics to nonequilibrium steady states. Using driven stochastic lattice gases, we ask whether consistent definitions of an effective chemical potential $\mu$, and an effective temperature $T_e$, are possible. These quantities are determined via zero-flux conditions of particles and energy between the driven system and a reservoir. For the models considered here, the fluxes are given in terms of certain stationary average densities, eliminating the need to perturb the system by actually exchanging particles; $\mu$ and $T_e$ are thereby obtained via open-circuit measurements, using a virtual reservoir. In the lattice gas with nearest-neighbor exclusion, temperature is not relevant, and we find that the effective chemical potential, a function of density and drive strength, satisfies the zeroth law, and correctly predicts the densities of coexisting systems. In the Katz-Lebowitz-Spohn driven lattice gas, both $\mu$ and $T_e$ need to be defined. We show analytically that the zeroth law is violated, and determine the size of the violations numerically. Our results highlight a fundamental inconsistency in the extension of thermodynamics to nonequilibrium steady states. [Preview Abstract] |
Monday, March 3, 2014 4:30PM - 4:42PM |
D16.00011: Fluctuation spectra in weakly modulated nonlinear systems Yaxing Zhang, Yukihiro Tadokoro, Mark Dykman We consider periodically modulated nonlinear systems and show that, along with the delta-peak at the modulation frequency, their spectral density of fluctuations can display extra peaks. The intensity of the peaks is quadratic in the modulation amplitude, for weak modulation. For systems where inertial effects can be disregarded, like an overdamped particle in a potential well, the peaks are generally located at zero frequency and at the modulation frequency. The widths of the peaks are characterized by the reciprocal correlation time of the system fluctuations in the absence of modulation and the noise correlation time. The spectra sensitively depend on the interrelation between these times and on the fluctuation intensity. They are determined not only by the fluctuations of the linear response, but also have a contribution from nonlinear response. The analytical results obtained for overdamped dynamical systems as well as two-state systems and systems with a threshold are in excellent agreement with numerical simulations. [Preview Abstract] |
Monday, March 3, 2014 4:42PM - 4:54PM |
D16.00012: Nontrivial Exponents in Record Statistics Eli Ben-Naim, Pearson Miller We investigate records in a growing sequence of identical and independently distributed random variables. The record equals the largest value in the sequence, and our focus is on the increment, defined as the difference between two successive records. We investigate sequences in which all increments decrease monotonically, and analyze the case where the random variables are drawn from a uniform distribution with compact support. We find that the fraction $I_N$ of sequences that exhibit this property decays algebraically with sequence length $N$, namely $I_N \sim N^{-\nu}$ as $N \rightarrow \infty$, and obtain the exponent $\nu = 0.317621\ldots$ using analytic methods. We also study the record distribution and the increment distribution. Whereas the former is a narrow distribution with an exponential tail, the latter is broad and has a power-law tail characterized by the exponent $\nu$. Empirical analysis of records in the sequence of waiting times between successive earthquakes is consistent with the theoretical results. [Preview Abstract] |
Monday, March 3, 2014 4:54PM - 5:06PM |
D16.00013: Lifetime and decay of seeded breathers in the FPU system Matthew Westley, Nicholas DeMeglio, Surajit Sen, T.R. Krishna Mohan The Fermi-Pasta-Ulam problem [1] consists of a chain of N oscillators with linear and nonlinear nearest neighbor interactions. Using velocity-Verlet integration, we study the evolution of the system after a perturbation that consists of a single stretched bond at the center of the chain [2-4]. This perturbation results in the localization of most of the system's energy in the center particles in the form of a ``breather'' up to reasonably long times, which leaks energy at a rate depending on the potential parameters and the perturbation amplitude. The breather eventually undergoes a catastrophic breakdown, releasing all of its energy into acoustic noise and solitary waves. We explore the conditions on the amplitude and the parameters $\alpha $, $\beta $ for which a seeded breather will be most or least stable. Also we show how the overlap or lack thereof between the breather's primary frequencies and the acoustic frequencies influences its long-time stability. \\[4pt] [1] E. Fermi, J. Pasta, and S. Ulam, Los Alamos Scientific Laboratory Report No. LA-1940 (1955).\\[0pt] [2] S. Flach and A. V. Gorbach, Phys. Rep. \textbf{467}, 1 (2008).\\[0pt] [3] A. J. Sievers and S. Takeno, Phys. Rev. Lett. \textbf{61}, 970 (1988).\\[0pt] [4] T. K. Mohan and S. Sen, Pramana \textbf{77}, 975 (2011). [Preview Abstract] |
Monday, March 3, 2014 5:06PM - 5:18PM |
D16.00014: Spontaneous symmetry breaking of action in complex systems Georgi Georgiev In simple systems the action has a single minimum for the motion of a particle along a geodesic, compared to all other paths. In complex systems, motion along a geodesic has higher action, compared to an infinite set of symmetric longer trajectories, due to constraints. For infinitely long paths, action rises to infinity. On this ``Mexican hat'' surface, a system spontaneously chooses one of the infinite number of minimum action trajectories, during its phase transition from a simple to a complex system. The initial geodesic path of a free particle is the ``vacuum,'' or ``ground state'' of the complex system. The action of the flow is minimized along a network as compared to motion in a different geometry. This leads to a flow network representation of a complex system, where the trajectories in the system are along flow paths with least action. A flow network implies a constant inflow and outflow of energy and can exist only in open systems far from equilibrium. We consider several examples in developing this formalism, which is useful for understanding and managing complex systems. [Preview Abstract] |
Monday, March 3, 2014 5:18PM - 5:30PM |
D16.00015: Thermodynamics of cellular statistical inference Alex Lang, Charles Fisher, Pankaj Mehta Successful organisms must be capable of accurately sensing the surrounding environment in order to locate nutrients and evade toxins or predators. However, single cell organisms face a multitude of limitations on their accuracy of sensing. Berg and Purcell first examined the canonical example of statistical limitations to cellular learning of a diffusing chemical and established a fundamental limit to statistical accuracy. Recent work has shown that the Berg and Purcell learning limit can be exceeded using Maximum Likelihood Estimation. Here, we recast the cellular sensing problem as a statistical inference problem and discuss the relationship between the efficiency of an estimator and its thermodynamic properties. We explicitly model a single non-equilibrium receptor and examine the constraints on statistical inference imposed by noisy biochemical networks. Our work shows that cells must balance sample number, specificity, and energy consumption when performing statistical inference. These tradeoffs place significant constraints on the practical implementation of statistical estimators in a cell. [Preview Abstract] |
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