Gavin E. Crooks

Postdoc Positions: Nanoscale thermodynamics.

We're always looking for talented postdocs and students. Currently there are postdoctoral positions open to study the nonequilbium thermodynamics of small systems, in particular the thermodynamics of molecular machines and nanoscale solar-energy conversion.

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News

2008-04-28: Cumulative Errata

A memorandum of miscellaneous minor mistakes.

2008-04-24: Lectures: Non-Equilibrium Fluctuation Theorems, from Jarzynski's identity and beyond

April 24, 29 and May 1, 433 Latimer, 2-3:30 PM Reading list:

• G. E. Crooks, Excursions in Statistical Mechanics (UC Berkeley PhD Thesis, 1999).
• G. Hummer and A. Szabo, Proc. Natl. Acad. Sci. USA 98, 3658-3661(2001)
• C. Bustamante, J. Liphardt and F. Ritort, "The non-equilibrium thermodynamics of small systems," Physics Today 58, 43-48(2005).

2008-04-14: Technical Note 004: Inequalities between the Jenson-Shannon and Jeffreys divergences

Jeffreys' J-divergence and the Jensen-Shannon divergence are shown to be related by an inequality that involves a transcendental function of the Jeffreys divergence.

2008-03-27: Published: Quantum operation time reversal

G.E. Crooks, G.E. Crooks, Phys. Rev. A 77 034101(4) (2008) doi:10.1103/PhysRevA.77.034101 The dynamics of an open quantum system can be described by a quantum operation: A linear, complete positive map of operators. Here, I exhibit a compact expression for the time reversal of a quantum operation, which is closely analogous to the time reversal of a classical Markov transition matrix. Since open quantum dynamics are stochastic, and not, in general, deterministic, the time reversal is not, in general, an inversion of the dynamics. Rather, the system relaxes toward equilibrium in both the forward and reverse time directions. The probability of a quantum trajectory and the conjugate, time reversed trajectory are related by the heat exchanged with the environment.

2008-03-27: Word of the Day: Super-duper-operator (n)

An operator is a linear map that acts on a vector space. A superoperator is an operator of an operator, an operator that acts on a vector space of operators. A super-duper-operator is an operator of an operator of an operator, an operator that acts on a vector space of superoperators.

2008-02-14: Technical Note 003v2: The Amoroso Distribution

The Amoroso distribution is the natural unification of the generalized gamma and generalized extreme value families of distributions. At least 40 distinct, named distributions (and as many synonyms) occur as special cases or limiting forms. Consequentially, this single simple functional form encapsulates and systematizes an extensive menagerie of interesting and common probability distributions.

2007-12-10: Office Translocation

New Office address: 260K Stanley Hall

2007-09-07: Published: Measuring thermodynamic length

G.E. Crooks, Phys. Rev. Lett. 99 100602 (2007)
doi:10.1103/PhysRevLett.99.100602

Research highlight: Nature Physics

Thermodynamic length is a metric distance between equilibrium thermodynamic states. Among other interesting properties, this metric asymptotically bounds the dissipation induced by a finite time transformation of a thermodynamic system. It is also connected to the Jensen-Shannon divergence, Fisher information, and Rao's entropy differential metric. Therefore, thermodynamic length is of central interest in understanding matter out of equilibrium. In this Letter, we will consider how to define thermodynamic length for a small system described by equilibrium statistical mechanics and how to measure thermodynamic length within a computer simulation. Surprisingly, Bennett's classic acceptance ratio method for measuring free energy differences also measures thermodynamic length. .

2007-07-03: Preprint: Bayesian estimates of free energies from nonequilibrium work data in the presence of instrument noise

Paul Maragakis, Felix Ritort, Carlos Bustamante, Martin Karplus, Gavin E. Crooks, arXiv:0707.0089 The Jarzynski equality and the fluctuation theorem relate equilibrium free energy differences to non-equilibrium measurements of the work. These relations extend to single-molecule experiments that have probed the finite-time thermodynamics of proteins and nucleic acids. The effects of experimental error and instrument noise have not previously been considered. Here, we present a Bayesian formalism for estimating free-energy changes from non-equilibrium work measurements that compensates for instrument noise and combines data from multiple driving protocols. We reanalyze a recent set of experiments in which a single RNA hairpin is unfolded and refolded using optical tweezers at three different rates. Interestingly, the fastest and farthest-from-equilibrium measurements contain the least instrumental noise, and therefore provide a more accurate estimate of the free energies than a few slow, more noisy, near-equilibrium measurements. The methods we propose here will extend the scope of single-molecule experiments; they can be used in the analysis of data from measurements with AFM, optical, and magnetic tweezers.

2007-06-13 Preprint: On the Quantum Jarzynski Identity

G.E. Crooks, arXiv:0706.1994 In this note, we will discuss how to compactly express and prove the Jarzynski identity for an open quantum system with dissipative dynamics. We will avoid explicitly measuring the work directly, which is tantamount to continuously monitoring the system, and instead measure the heat flow from the environment. We represent the measurement of heat flow with Hermitian map superoperators that act on the system density matrix. Hermitian maps provide a convenient and compact representation of sequential measurement and correlation functions.

2007-05-20: Technical Notes

2007-04-27: Published: Beyond Boltzmann-Gibbs statistics: Maximum entropy hyperensembles out-of-equilibrium

G.E. Crooks, Phys. Rev. E 75, 041119 (2007) What is the best description that we can construct of a thermodynamic system that is not in equilibrium, given only one, or a few, extra parameters over and above those needed for a description of the same system at equilibrium? Here, we argue the most appropriate additional parameter is the nonequilibrium entropy of the system. Moreover, we should not attempt to estimate the probability distribution of the system directly, but rather the metaprobability (or hyperensemble) that the system is described by a particular probability distribution. The result is an entropic distribution with two parameters, one a nonequilibrium temperature, and the other a measure of distance from equilibrium. This dispersion parameter smoothly interpolates between certainty of a canonical distribution at equilibrium and great uncertainty as to the probability distribution as we move away from equilibrium. We deduce that, in general, large, rare fluctuations become far more common as we move away from equilibrium.

2007-04-09: Gratuitous Link: David Crooks

Bohemian artist / Bohemian scientist.

2007-04-01: Random Quotes

Life is short and the alphabet shorter.
C.T.J. Dobson

In this context the real numbers are called scalars. The only reason for not calling them just "numbers", which would adequately distinguish them from vectors, is that for historical reasons nobody else does, and in mathematics, as in other languages, the idea is to be understood.
C.T.J. Dobson

Substitute damn every time you're inclined to write very; your editor will delete it and the writing will be just as it should be.
Mark Twain

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