21 research outputs found
Quantifying hidden order out of equilibrium
While the equilibrium properties, states, and phase transitions of
interacting systems are well described by statistical mechanics, the lack of
suitable state parameters has hindered the understanding of non-equilibrium
phenomena in diverse settings, from glasses to driven systems to biology. The
length of a losslessly compressed data file is a direct measure of its
information content: The more ordered the data is, the lower its information
content and the shorter the length of its encoding can be made. Here, we
describe how data compression enables the quantification of order in
non-equilibrium and equilibrium many-body systems, both discrete and
continuous, even when the underlying form of order is unknown. We consider
absorbing state models on and off-lattice, as well as a system of active
Brownian particles undergoing motility-induced phase separation. The technique
reliably identifies non-equilibrium phase transitions, determines their
character, quantitatively predicts certain critical exponents without prior
knowledge of the order parameters, and reveals previously unknown ordering
phenomena. This technique should provide a quantitative measure of organization
in condensed matter and other systems exhibiting collective phase transitions
in and out of equilibrium
Explicit Rational Function Solutions for the Power Spectral Density of Stochastic Linear Time-Invariant Systems
Stochasticity plays a central role in nearly every biological process, and
the noise power spectral density (PSD) is a critical tool for understanding
variability and information processing in living systems. In steady-state, many
such processes can be described by stochastic linear time-invariant (LTI)
systems driven by Gaussian white noise, whose PSD can be concisely expressed in
terms of their Jacobian, dispersion, and diffusion matrices, fully defining the
statistical properties of the system's dynamics at steady-state. Upon expansion
of this expression, one finds that the PSD is a complex rational function of
the frequency. Here, we arrive at a recursive Leverrier-Faddeev-type algorithm
for the exact computation of the rational function coefficients, as well as
compact element-wise solutions for the auto- and cross-spectrum that are useful
in the analytical computation of the PSD in dimensions n=2,3,4. Crucially, both
our solutions are free of matrix inverses. We illustrate our recursive and
element-wise solutions by considering the stochastic dynamics of neural systems
models, namely Fitzhugh-Nagumo (n=2), Hindmarsh-Rose (n=3), Wilson-Cowan (n=4),
and the Stabilized Supralinear Network (n=22), as well as of an evolutionary
game-theoretic model with mutations (n=5,31)
Bacteria Through Obstacles: Unifying Fluxes, Entropy Production, and Extractable Work in Living Active Matter
Thermodynamic equilibrium is a unique state characterized by time-reversal
symmetry, which enforces zero fluxes and prohibits work extraction from a
single thermal bath. By virtue of being microscopically out of equilibrium,
active matter challenges these defining characteristics of thermodynamic
equilibrium. Although time irreversibility, fluxes, and extractable work have
been observed separately in various non-equilibrium systems, a comprehensive
understanding of these quantities and their interrelationship in the context of
living matter remains elusive. Here, by combining experiments, simulations, and
theory, we study the correlation between these three quantities in a single
system consisting of swimming Escherichia coli navigating through funnel-shaped
obstacles. We show that the interplay between geometric constraints and
bacterial swimming breaks time-reversal symmetry, leading to the emergence of
local mass fluxes. Using an harmonically trapped colloid coupled weakly to
bacterial motion, we demonstrate that the amount of extractable work depends on
the deviation from equilibrium as quantified by fluxes and entropy production.
We propose a minimal mechanical model and a generalized mass transfer relation
for bacterial rectification that quantitatively explains experimental
observations. Our study provides a microscopic understanding of bacterial
rectification and uncovers the intrinsic relation between time irreversibility,
fluxes, and extractable work in living systems far from equilibrium.Comment: 19 pages, 10 figure
Turning intractable counting into sampling: Computing the configurational entropy of three-dimensional jammed packings.
We present a numerical calculation of the total number of disordered jammed configurations Ω of N repulsive, three-dimensional spheres in a fixed volume V. To make these calculations tractable, we increase the computational efficiency of the approach of Xu et al. [Phys. Rev. Lett. 106, 245502 (2011)10.1103/PhysRevLett.106.245502] and Asenjo et al. [Phys. Rev. Lett. 112, 098002 (2014)10.1103/PhysRevLett.112.098002] and we extend the method to allow computation of the configurational entropy as a function of pressure. The approach that we use computes the configurational entropy by sampling the absolute volume of basins of attraction of the stable packings in the potential energy landscape. We find a surprisingly strong correlation between the pressure of a configuration and the volume of its basin of attraction in the potential energy landscape. This relation is well described by a power law. Our methodology to compute the number of minima in the potential energy landscape should be applicable to a wide range of other enumeration problems in statistical physics, string theory, cosmology, and machine learning that aim to find the distribution of the extrema of a scalar cost function that depends on many degrees of freedom.We acknowledge useful discussions with Daniel Asenjo, Carl Goodrich, Silke Henkes, and Fabien Paillusson. S.M. acknowledges financial support by the Gates Cambridge Scholarship. K.J.S. acknowledges support by the Swiss National Science Foundation under Grant No. P2EZP2-152188 and No. P300P2-161078. J.D.S. acknowledges support by Marie Curie Grant 275544. D.F. and D.J.W. acknowledge support by EPSRC Programme Grant EP/I001352/1, by EPSRC grant EP/I000844/1 (D.F.) and ERC Advanced Grant RG59508 (D.J.W.)This is the author accepted manuscript. The final version is available from the American Physical Society via http://dx.doi.org/10.1103/PhysRevE.93.01290
Estimating random close packing in polydisperse and bidisperse hard spheres via an equilibrium model of crowding
We show that an analogy between crowding in fluid and jammed phases of hard
spheres captures the density dependence of the kissing number for a family of
numerically generated jammed states. We extend this analogy to jams of mixtures
of hard spheres in dimensions, and thus obtain an estimate of the random
close packing (RCP) volume fraction, , as a function of
size polydispersity. We first consider mixtures of particle sizes with discrete
distributions. For binary systems, we show agreement between our predictions
and simulations, using both our own and results reported in previous works, as
well as agreement with recent experiments from the literature. We then apply
our approach to systems with continuous polydispersity, using three different
particle size distributions, namely the log-normal, Gamma, and truncated
power-law distributions. In all cases, we observe agreement between our
theoretical findings and numerical results up to rather large polydispersities
for all particle size distributions, when using as reference our own
simulations and results from the literature. In particular, we find
to increase monotonically with the relative standard
deviation, , of the distribution, and to saturate at a value that
always remains below 1. A perturbative expansion yields a closed-form
expression for that quantitatively captures a
distribution-independent regime for . Beyond that regime, we
show that the gradual loss in agreement is tied to the growth of the skewness
of size distributions
ColabFit Exchange: open-access datasets for data-driven interatomic potentials
Data-driven (DD) interatomic potentials (IPs) trained on large collections of
first principles calculations are rapidly becoming essential tools in the
fields of computational materials science and chemistry for performing
atomic-scale simulations. Despite this, apart from a few notable exceptions,
there is a distinct lack of well-organized, public datasets in common formats
available for use with IP development. This deficiency precludes the research
community from implementing widespread benchmarking, which is essential for
gaining insight into model performance and transferability, while also limiting
the development of more general, or even universal, IPs. To address this issue,
we introduce the ColabFit Exchange, the first database providing open access to
a large collection of systematically organized datasets from multiple domains
that is especially designed for IP development. The ColabFit Exchange is
publicly available at \url{https://colabfit.org/}, providing a web-based
interface for exploring, downloading, and contributing datasets. Composed of
data collected from the literature or provided by community researchers, the
ColabFit Exchange consists of 106 datasets spanning nearly 70,000 unique
chemistries, and is intended to continuously grow. In addition to outlining the
software framework used for constructing and accessing the ColabFit Exchange,
we also provide analyses of data, quantifying the diversity and proposing
metrics for assessing the relative quality and atomic environment coverage of
different datasets. Finally, we demonstrate an end-to-end IP development
pipeline, utilizing datasets from the ColabFit Exchange, fitting tools from the
KLIFF software package, and validation tests provided by the OpenKIM framework
Structural analysis of high-dimensional basins of attraction.
We propose an efficient Monte Carlo method for the computation of the volumes of high-dimensional bodies with arbitrary shape. We start with a region of known volume within the interior of the manifold and then use the multistate Bennett acceptance-ratio method to compute the dimensionless free-energy difference between a series of equilibrium simulations performed within this object. The method produces results that are in excellent agreement with thermodynamic integration, as well as a direct estimate of the associated statistical uncertainties. The histogram method also allows us to directly obtain an estimate of the interior radial probability density profile, thus yielding useful insight into the structural properties of such a high-dimensional body. We illustrate the method by analyzing the effect of structural disorder on the basins of attraction of mechanically stable packings of soft repulsive spheres.EPSRC No. EP/I001352/1 and. EP/I000844/1
EU Marie Curie Grant 275544
ERC Grant RG5950