Tech. Note: Field Guide to Continuous Probability Distributions

Unimodal distributions

Version: 0.7 beta

In a desperate attempt to preserve my own sanity, a survey of probability distributions used to describe a single, continuous, unimodal, univariate random variable.

Whats New: Added Hohlfeld distribution. Added appendix on limits. Reformatted and rationalized distribution hierarchy diagrams. Fixed typos and improved formatting. Thanks to Phill Geissler.

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Preprint: Sampling an Ensemble of Low-dissipation Protocols for Nonequilibrium Control

Todd R. Gingrich, Grant M. Rotskoff, Gavin E. Crooks, Phillip L. Geissler arXiv:1602.01459

[ Full text | arXiv ]isingpath


The development of sophisticated experimental tools for controlling nanoscale systems has motivated efforts to design driving protocols which minimize the energy dissipated to the environment. Computational models are a crucial ingredient in this practical challenge and we describe a general method for sampling an ensemble of finite-time, nonequilibrium protocols biased towards a low average dissipation. We show that this scheme can be carried out very efficiently in several limiting cases and analyze the computational efficiency of the algorithm for a simple model system. As an application, we sample the ensemble of low-dissipation protocols that invert the magnetization of the 2D Ising model and explore how the diversity of the protocols varies in response to constraints on the average dissipation.

Celebrating 50,000 Publications: Physical Review E Milestones

Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences
Gavin E. Crooks Phys. Rev. E 60, 2721 (2000)

Physical Review E published its 50,000th paper in September 2015. To celebrate this, the journal presents a series of milestone papers that were published since its inception in 1993. This is an eclectic collection of papers that made significant contributions to their field, chosen by the editors. A new milestone will be added each week.

Article: Optimal control in nonequilibrium systems: Dynamic Riemannian geometry of the Ising model

Grant M. Rotskoff, Gavin E. Crooks, Phys. Rev. E, 92, 060102 (2015)

[ Full text | Journal| arXiv ]


A general understanding of optimal control in nonequilibrium systems would illuminate the operational principles of biological and artificial nanoscale machines. Recent work has shown that a system driven out of equilibrium by a linear response protocol is endowed with a Riemannian metric related to generalized susceptibilities, and that geodesics on this manifold are the nonequilibrium control protocols with the lowest achievable dissipation. While this elegant mathematical framework has inspired numerous studies of exactly solvable systems, no description of the thermodynamic geometry yet exists when the metric cannot be derived analytically. Herein, we numerically construct the dynamic metric of the two-dimensional Ising model in order to study optimal protocols for reversing the net magnetization.

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Grand East Coast Tour (Oct/Nov 2015)

Optimal Thermodynamic Control and the Dynamic Riemannian Geometry of Ising magnets
Stonybrook University
Friday Oct. 30, 2:30pm, Laufer Center lecture hall

D.E. Shaw Research
Monday Nov. 2, 12:00

MIT – Physics Colloquium
Guest of the Physics Graduate Student Council
Thursday Nov 5th, 4:00 pm, Room 10-250

Edgestream Partners
Monday Nov 9th, 1:00 pm

U. of Maryland, College Park – Statistical Physics Seminar
Tuesday Nov 10th, 1:15 pm, Room 1116 IPST Building 085.

NIH – Statistical Physics Seminar
Thursday Nov 12th, 11:00 am

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Seminar @ Memorial Sloan Kettering Cancer Center

maxMolecular Machines: Optimal thermodynamic control and The thermodynamic cost of nostalgia

10:30-11:30am, May 7th 2015

ZRC 105, 417 East 68th Street New York, NY 10065

paper Thermodynamic metrics and optimal paths,
David A. Sivak, Gavin E. Crooks, Phys. Rev. Lett., 108, 190602 (2012)
[ Full text | Journal | More ]
title The geometry of thermodynamic control,
Patrick R. Zulkowski, David A. Sivak, Gavin E. Crooks and Michael R. DeWeese, Phys. Rev. E, 86, 041148 (2012)
[ Full text | Journal | More ]

Princeton Lectures on The Dynamics of Disorder

Over the next 2 weeks I will be lecturing at the Princeton Center for Theoretical Science on non-equilibrium statistical dynamics.

Lecture notes and other resources

== The Fluctuations of Dissipation ==
1:00-2:00 Tuesday, April 7th, A06 Jadwin Hall
Foundations of non-equilibrium statistical dynamics. I’ll explain the basics of fluctuations theorems and the Jarzynski’s identity.

== The Ambiguity of Time’s Arrow (Public Lecture) ==
8:00pm, A10 Jadwin Hall

== The Geometry of Thermodynamics ==
1:00-2:00 Tuesday, April 14th, A06 Jadwin Hall

== Entropy, information and Maxwell’s Demon ==
1:00-2:00 Thursday, April 16th 17th, A06 Jadwin Hall
Maxwell’s demon, Szilard’s engine, Landauer’s principle, and the feedback fluctuation theorems.


“And then there’s quantum, of course.” The monk sighed. “There’s always bloody quantum.” — Night Watch, Terry Pratchett

Berkeley Lectures on the Dynamics of Disorder

Starting this Thursday, I will be giving 3 guest introductory lectures on the non-equilibrium statistical dynamics of small systems, as part of Phill Geissler’s Advanced Statistical Mechanics course.

Lecture notes and other resources

Tentative syllabi:

== The fluctuations of dissipation ==
2:00-3:30 Thursday, March 12th, 425 Latimer
Equilibrium and disequilibrium; fluctuations theorems and the Jarzynski’s identity; experiments and observations.

== Entropy and information ==
2:00-3:30 Tuesday, March 17th, 425 Latimer
Maxwell’s demon, Szilard’s engine, Landauer’s principle, and the feedback fluctuation theorems.

== Perturbation and response ==
2:00-3:30 Thursday, March 19th, 425 Latimer
Perturbations and response; fluctuations and dissipation; from fluctuation theorems to linear response; the geometry of thermodynamics.

Announcement: Enrollment open for Kavli Scientist-Writer workshops

Enrollment is now open for the second year of the Kavli Scientist-Writer workshops @ NYU. I had the honor of attending the inaugural class, and it was great. As my fellow alumni puts it:

“The best course I’ve had since college… Scientists sorely need instruction of this kind, whether they try to write for the public or only for their peers. Every department at every institution should have this kind of course, and the organizers of this first pass did a fantastic job.”

– Jacqueline Gotteib, Kavli Institute of Brain Science, Columbia University

Our job, as scientists, is to explore strange new ideas, to seek out new knowledge and new understanding, to boldly experiment where no scientist has tinkered before. But none of that counts, if we don’t come back and tell people what we have discovered. And it dosn’t count as telling people if we write turgid incomprehensible prose that nobody will read or understand.

Article: Scaling laws governing stochastic growth and division of single bacterial cells

Srividya Iyer-Biswas, Charles S. Wright, Jonathan T. Henry, Klevin Lo, Stanislav Burov, Yihan Lin, Gavin E. Crooks, Sean Crosson, Aaron R. Dinner, Norbert F. Scherer, Proc. Natl. Acad. Sci. U.S.A. (2014)

[ Full text | Journal | arXiv ]cell

This is the experimental paper that logically (but, alas, not chronologically) precedes the companion theory paper.

Abstract: Uncovering the quantitative laws that govern the growth and division of single cells remains a major challenge. Using a unique combination of technologies that yields unprecedented statistical precision, we find that the sizes of individual Caulobacter crescentus cells increase exponentially in time. We also establish that they divide upon reaching a critical multiple (≈1.8) of their initial sizes, rather than an absolute size. We show that when the temperature is varied, the growth and division timescales scale proportionally with each other over the physiological temperature range. Strikingly, the cell-size and division-time distributions can both be rescaled by their mean values such that the condition-specific distributions collapse to universal curves. We account for these observations with a minimal stochastic model that is based on an autocatalytic cycle. It predicts the scalings, as well as specific functional forms for the universal curves. Our experimental and theoretical analysis reveals a simple physical principle governing these complex biological processes: a single temperature-dependent scale of cellular time governs the stochastic dynamics of growth and division in balanced growth conditions.