MSci Project Proposal Form 2010-2011
Project Code: CMTH-Tangney-1
Project title: Exploring the statistical behaviour of small systems far from equilibrium
Supervisor: Dr Paul Tangney
Assessor: Dr Arash Mostofi
Telephone: Ex. 4 8155
Telephone: Ex. 4 8154
E-mail: p.tangney
E-mail: a.mostofi
Research Group: CMTH
Research Group: CMTH
Project Summary:
The last fifteen years has seen rapid development in the field of statistical physics of far-fromequilibrium systems. The story of this acceleration of progress begins with the first presentation
of a Fluctuation Theorem by Evans, Cohen, and Morriss in 1993 [1]. They showed that
fluctuations that violate the second law of thermodynamics can occur, however, they also
showed that the probability of a net decrease in entropy persisting for a time T decreases very
quickly with T so that on long time scales it is overwhelming likely that entropy increases.
Another theoretical result that had a major impact in this field was provided by Jarzynski in
1997[2]. He imagined a system being driven between two states labeled A and B by an arbitrary
non-equilibrium process. For example, the system in question might be a long molecule and A
might be its folded state and B its unfolded state. There are an infinite number of ways in which
one can force the molecule to fold and unfold and the work done during each of these realisations
is different. Jarzynski related the average of the exponential of the work done over all these
realisations to the equilibrium free energies of states A and B. In other words, he provided a
statistical relationship between the dynamics of processes that occur far from equilibrium and
equilibrium properties - an astonishing result.
There are several other landmarks among the hundreds (perhaps thousands) of papers that have
followed on from this early work. There is now a large body of experimental, theoretical and
computational work that attests to the validity of the Fluctuation theorem and Jarzynski's
relation. However, there is also some controversy. There are those that doubt the rigour of
existing proofs of Jarzynski's equation, in particular, and some who doubt that this equations is
even correct in any useful sense.
This project will explore aspects of the foundations of this new area of non-equilibrium statistical
mechanics and seek resolutions to some of these controversies.
[1] "Probability of second law violations in shearing steady states", D. J. Evans, E. G. D. Cohen, and G. P. Morriss, Phys.
Rev. Lett., 71, 2401 (1993). [2] "Non-equilibrium equality for free-energy differences", C. Jarzynski, Phys. Rev. Lett. 78,
2690 (1997).
Experimental component:
0%
Computational component: 0-10%
Theoretical component:
90-100%
Is the MSci Project eligible for students on the MSci
Physics with Theoretical Physics Degree: YES
Are workshop facilities required: NO
Suggested reading:

"Comparison of far-from-equilibrium work relations", C. Jarzynski, Comptes Rendus Physique, 8, 495 (2007).

Denis Evans web page provides an excellent list of review articles, slides etc..
http://rsc.anu.edu.au/~evans/index.php
Google search terms: "Jarzynski relation", "Jarzynski equality", "Fluctuation theorem", "Crooks fluctuation
theorem", "Non equilibrium work theorems", "wwork fluctuation theorems"
Imperial College of Science, Technology, and Medicine