Bespoke research in the fields of Quantum Machine Learning, Non-equilibrium thermodynamics, and the Physics of Information. Currently localized at Rigetti Quantum Computers, Berkeley, CA

# Category Archives: -New-

# Tech. Note 009 v0.7: On Measures of Information and Entropy 009 v0.7

A brief overview of information measures on classical, discrete probability distributions. 009 v0.7 [ Full Text ]

# Tech. Note: Field Guide to Continuous Probability Distributions v0.11 beta

Version: 0.11 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 hyperbola, hyperbolic, Halphen, Halphen B, inverse Halphen B, generalized Halphen, Sichel, Appell Beta, K and generalized K distributions. Thanks to Saralees Nadarajah and Harish Vangala

[ Full Text ]

# Article: Geometric approach to optimal nonequilibrium control: Minimizing dissipation in nanomagnetic spin systems

Grant M. Rotskoff, Gavin E. Crooks, Eric Vanden-Eijnden

Phys. Rev. E 95 012148 (2017)

[Full text | Journal | arXiv ]

**Abstract**:

Optimal control of nanomagnets has become an urgent problem for the field of spintronics as technological tools approach thermodynamically determined limits of efficiency. In complex, fluctuating systems, like nanomagnetic bits, finding optimal protocols is challenging, requiring detailed information about the dynamical fluctuations of the controlled system. We provide a new, physically transparent derivation of a metric tensor for which the length of a protocol is proportional to its dissipation. This perspective simplifies nonequilibrium optimization problems by recasting them in a geometric language. We then describe a numerical method, an instance of geometric minimum action methods, that enables computation of geodesics even when the number of control parameters is large. We apply these methods to two models of nanomagnetic bits: a simple Landau-Lifshitz-Gilbert description of a single magnetic spin controlled by two orthogonal magnetic fields and a two dimensional Ising model in which the field is spatially controlled. These calculations reveal nontrivial protocols for bit erasure and reversal, providing important, experimentally testable predictions for ultra-low power computing.

# Preprint: Marginal and Conditional Second Laws of Thermodynamics

Gavin E. Crooks, Susanne Still arXiv:1611.04628

**Abstract**:

We consider the entropy production of a strongly coupled bipartite system. The total entropy production can be partitioned into various components, which we use to define local versions of the Second Law that are valid without the usual idealizations. The key insight is that the joint trajectory probability of interacting systems can be split into terms representing the dynamics of the individual systems without feedback.

# Article: Thermodynamic geometry of minimum-dissipation driven barrier crossing

David Sivak, Gavin E. Crooks Phys. Rev. E 94(5):052106 (2016)

[Full text | Journal | arXiv ]

The last paper from our time working together in Berkeley. Ironically, also the first project David worked on during his postdoc. But a 7 year lag from inception to completion matches my previous records [Crooks2008a, Crooks2008b].

**Abstract**:

We explore the thermodynamic geometry of a simple system that models the bistable dynamics of nucleic acid hairpins in single molecule force-extension experiments. Near equilibrium, optimal (minimum-dissipation) driving protocols are governed by a generalized linear response friction coefficient. Our analysis demonstrates that the friction coefficient of the driving protocols is sharply peaked at the interface between metastable regions, which leads to minimum-dissipation protocols that drive rapidly within a metastable basin, but then linger longest at the interface, giving thermal fluctuations maximal time to kick the system over the barrier. Intuitively, the same principle applies generically in free energy estimation (both in steered molecular dynamics simulations and in single-molecule experiments), provides a design principle for the construction of thermodynamically efficient coupling between stochastic objects, and makes a prediction regarding the construction of evolved biomolecular motors.

# Tech. Note: Field Guide to Continuous Probability Distributions v0.9 beta

Version: 0.9 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 pseudo Voigt,and Student’s t_3 distributions. Reparameterized hyperbolic sine distribution. Derived limit of Unit gamma to log-normal.Corrected spelling of “arrises” (sharp edges formed by the meeting of surfaces) to “arises” (emerge; become apparent). Added Moyal distribution, a special case of the gamma-exponential distribution. Corrected spelling of “principle” to “principal” (Kudos: Matthew Hankins, Mara Averick).

[ Full Text ]

# Article: Near-optimal protocols in complex nonequilibrium transformations

Todd R. Gingrich, Grant M. Rotskoff, Gavin E. Crooks, Phillip L. Geissler Proc. Natl. Acad. Sci. U.S.A. (2016)

**Abstract**:

The development of sophisticated experimental means to control nanoscale systems has motivated efforts to design driving protocols that minimize the energy dissipated to the environment. Computational models are a crucial tool in this practical challenge. We describe a general method for sampling an ensemble of finite-time, nonequilibrium protocols biased toward a low average dissipation. We show that this scheme can be carried out very efficiently in several limiting cases. As an application, we sample the ensemble of low-dissipation protocols that invert the magnetization of a 2D Ising model and explore how the diversity of the protocols varies in response to constraints on the average dissipation. In this example, we find that there is a large set of protocols with average dissipation close to the optimal value, which we argue is a general phenomenon.

# WebLogo 3.5 Released

3.5 (2016-07-24) [Gavin Crooks, Melissa Fabros]

* Moved source control from GoogleCode to GitHub

* Switched from Subversion as version control method to Git

* Refactor html to optimize WebLogo use on mobile computing devices

* Add feature to open sequence files via file sharing URL link from Web application and command line

* Updated documentation

* PEP8ify all python files to solve formatting issues. (Kudos:Gert Hulselmans)

* Expose additonal LogoOptions via CLI options (Kudos:Gert Hulselmans)

* Fixed performance issue by limiting size of data that can be pasted into html form

Use file upload instead. (Kudos: Peter Cherepanov)

* Add ability to custom color every stack (Kudos: Kale Kundert)

* Weblogo 3.5 runs under python 2.6, 2.7, 3.2, 3.3, 3.4 & 3.5

* Fixed bugs for compatible with Python 3 (Kudos: Gert Hulselmans, Teshome Mulugeta)

* Miscellaneous minor bug fixes and refactoring (Kudos: David Kelley)

### Quote

Let this book be dedicated to the chemists of the newer generation, who will not wish to reject all inferences from conjecture or surmise, but who will not care to speculate concerning that which may be surely known. The fascination of a growing science lies in the work of the pioneers at the very borderland of the unknown, but to reach this frontier one must pass over well traveled roads; of these one of the safest and surest is the broad road of thermodynamics.

Gilbert Lewis and Merle Randall, Thermodynamics (1923)

# Physics Colloquium @ UC Davis, Mon Apr 25 2016

*Optimal Thermodynamic Control and the Dynamic Riemannian Geometry of Ising magnets*

55 Roessler Hall, UC Davis, 4:10 – 5:30 PM, Monday 25th April 2016

**Papers, Slides, Multimedia**

slidesOptimal Thermodynamic Control and the Dynamic Riemannian Geometry of Ising magnets

paperDynamic Riemannian Geometry of the Ising Model

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

paperThermodynamic metrics and optimal paths

David A. Sivak, Gavin E. Crooks, Phys. Rev. Lett., 108, 190602 (2012)

# I tweet, therefore I am.

# Tech. Note: Field Guide to Continuous Probability 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.

[ Full Text ]

# 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

**Abstract**:

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.