Denis Evans' Professional Page.


This page includes information which is additional to my official Research School of Chemistry Home Page entry and

to my hiking/bushwalking pages at:


Snowgums above Dead Horse Gap (June, 2001).

Statistical Mechanics

We are known for deriving and experimentally confirming the Fluctuation Theorem.

This Theorem gives an elegant extension of the Second Law of Thermodynamics,

so that it applies to finite systems observed for finite times. It also provides the first proof of the Second Law of Thermodynamics - it ceases to be a "Law".

This theorem relates the probabilities of observing time averaged values of a generalized entropy production, namely the dissipation function,

for a period of time, t, equal to an arbitrary value B, relative to -B. This ratio is exponential in the length of the averaging time t, and the number of degrees of freedom in the system - since entropy production is extensive. In the definition of the dissipation function f(G,0) is the initial phase space distribution function dQ/dt is the rate of heat gained or lost per unit time by the system of interest from a thermostat. The thermostat is viewed as being much larger than the system of interest and can therefore be regarded as being in thermodynamic eqilibrium at a temperature Tres.

The Theorem resolves the paradox of how time-reversible microscopic dynamics leads, to irreversible macroscopic behaviour. It also implies that as devices are made smaller and smaller the probability that they will run thermodynamically in reverse to what one would expect, increases exponentially with decreasing system size and observation time.

This result is exact for classical systems and quantum anologues are known.

Scientific news articles, popular press and news reports on the Fluctuation Theorem, October 2002.

See also C. Bustamante, J. Liphardt, and F. Ritort, Physics Today, 58, no 7, page 43-48, 2005.


The Second Law Inequality is a simple consequence of the Fluctuation Theorem.

It says that the generalized entropy production can be negative but the time average of the ensemble average cannot be negative.

(Searles and Evans, Aust. J. Chem., 57,1119(2004).)

The Dissipation Theorem says that the nonlinear response of an arbitrary phase variable can be calculated from the time integral of the nonequilibrium transient time correlation function of the phase variable with the dissipation function

(Evans, Searles &Williams, J.Chem.Phys., 128, 014504(2008), ibid 128, 249901(2008).):

Finally the Relaxation Theorem says that if an arbitrary initial ensemble of ergodic Hamiltonian systems is in contact with a heat bath and there is a decay of temporal correlations, then the system will at long times, relax to the Maxwell-Boltzmann distribution. Further, this distribution has zero dissipation everywhere in phase space. For such systems no other distribution has zero dissipation everywhere.

Each of these results is exact arbitrarily far from equilibrium and independent of system size.

Liquid State Chemical Physics Research Group

Group members include

Dr Stephen Williams.

Here are two group photos (2001). In the first photo we have from left to right, Owen Jepps (former student), Dr Jerome Delhommelle , Emil Mittag (former student) and Dr Janka Petravic. In the second photo we have Emil, Jerome, Denis and Janka.

The group in 2005. Left to right: James Reid, Stephen Williams and Denis.

We have longstanding and close links with Dr Debra Searles, Griffith University Queensland, and Dr Edie Sevick in the Research School of Chemistry ANU.


My Thomson H-index is 55. My Scholar Google H-index is 62 (8/6/1014).

My Scholar Google web site is here. This Scholar Google site has been vetted by me as accurate and contains much information including the publications as well as various citation data.

CV, lecture notes and publications

  • List of Publications, Curriculum Vitae, Annual Report, Liquid State Chemical Physics Group , Official home page.
  • Denis Evans' Boltzmann number is 4: Boltzmann 0; Ehrenfest (student) 1; Uhlenbeck (student) 2; Cohen (mentor) 3; Evans (mentor) 4.
  • Denis Evans' Einstein number is 4, but there is another publication route giving an Einstein Number of 6- but this route involves some really great scientists.

  • Papers and lectures on the NonEquilibrium Statistical Mechanics
  • Lecture Notes (215Kb) on "Nonequilibrium Statistical Mechanics and Lyapunov Instability" (In Adobe Acrobat format. Obtain the reader free from Adobe).
  • Lecture Notes (332Kb) on "Nonlinear Response Theory of Non-Autonomous Systems" (Acrobat format).
  • Lecture 1 (65Kb), Lecture 2 (65Kb) and Lecture 3 (98Kb), on "NonEquilibrium Statistical Mechanics and Lyapunov Instability" by myself and Debra Searles (Acrobat format).
  • Paper on "Approach to the nonequilibrium time-periodic state in a steady shear flow model" , Mol. Phys., 95, 219-231 (1998). .
  • Paper on "Configurational Temperature, Verification of Monte Carlo Simulations" J. Chem. Phys., 109, 6519-6522(1998) J. Chem.
  • Phys.2000/2001 Boys-Rahman lecture of the Royal Society of Chemistry (London).
  • A paper on the entropy of nonequilibrium steady states, with Lamberto Rondoni, J. Stat. Phys, 109, 895-920, (2002).
  • New observations concerning time reversible deterministic thermostats - why the standard forms for deterministic thermostats are unique - J. Chem. Phys., 133, 104106-4(2010)
  • Real audio, and Lecture II on Fluctuation Theorems with (24MB) Real audio. These lectures can be downloaded as podcasts from the Apple iTunes store.
  • Lectures (video) at the 2006 Durham International Conference on "Dynamical Systems and Statistical Mechanics" by Debra Searles, Lamberto Rondoni and myself are searchable on Apple iTunes search for Denis Evans or Fluctuation Theorem.
  • A (video) lecture on the Fluctuation and Dissipation Theorems, given in the Research School of Information Sciences and Engineering, Canberra Australia, August 2007. The Power Point presentation is here.
  • Statistical Mechanics of Time Independent Non-Dissipative Nonequilibrium States - but this does involve the Transient Fluctuation Theorem.
  • Two lectures on Chaos and NonEquilibrium statistical mechanics given at the Institut Henri Poincare, October 8, 2006. Lecture 1 and Lecture 2.
  • Three lectures at Oak Ridge National Laboratory, April 22, 2008: lectures 1, 2, 3.
  • Australian National University, Physics and Chemistry honours year undergraduate lectures on: "The Foundations of Statistical Thermodynamics"
  • The rheology of crystals.
    Papers on the Fluctuation Theorem and related topics - Scientific news articles and popular press reports on the Fluctuation Theorem, October 2002.
  • The first paper on any Fluctuation Theorem: ECM2, Evans, Cohen & Morriss, Phys. Rev. Letts., 71, 2401(1993).
  • Paper “A local fluctuation theorem”, J. Chem. Phys., 115 , 2033–2037 (2001), eprint archive cond-mat/9901256.
  • Paper on "The Fluctuation Theorem for Stochastic Systems", Phys Rev EZ6305, (1999), eprint archive cond-mat/9901258.
  • Paper on "The Fluctuation Theorem and Green-Kubo Relations", J Chem Phys, 112,9727(2000), by Debra Searles and myself
  • Draft paper on the Fluctuation Theorem for heat flow.
  • Review : "The Fluctuation Theorem" by Denis J Evans and Debra J Searles, Advances in Physics, 51, 1529-1585(2002).
  • Experimental test of the Integrated Fluctuation Theorem using optical tweezers, Phys. Rev. Lett. 89, 050601 (2002). An animation of the experiment.
  • A rigorous derivation of the Transient Fluctuation Theorem using Lyapunov rather than Gibbs, weights, Physica D, 187, 326-337(2002).
  • A paper by Denis J. Evans, on NonEquilibrium Free Energy Theorems, Molecular Physics, 101, 1551(2003).
  • A Fluctuation Theorem for time dependent dissipative fields, Phys. Rev. E 67, 026113 (2003) .
  • A talk Thermodynamic limits to nanomachines Australian Academy of Science International Symposium on:
    Nanoscience – where physics, chemistry and biology collide, Canberra, 2 May 2003.
  • Download a talk on the Fluctuation Theorem by Debra Searles.
  • Preprint of a proof that the Gallavotti Cohen FT converges ever more slowly as equilibrium is approached, archived at, and Phys. Rev. E 71, 056120 (2005).
  • First experimental confirmation of the (detailed) Transient Fluctuation Theorem, Phys. Rev. Lett., 92, 140601(2004).
  • Explicit demonstration of the independence of the Fluctuation Theorem to details of thermostatting mechanism, Phys. Rev. E 70, 066113 (2004).
  • Demonstration that van Zon and Cohen FT is an example of the Gallavotti-Cohen FT, to appear Molecular Simulation.
  • First experimental confirmation of the steady state FT by observing the response of an electrical circuit to thermal noise. Nonequilibrium fluctuations in a resistor by: Nicolas Garnier, Sergio Ciliberto: .
  • Experimental confirmation of the steady state FT for a colloidal particle in an optical trap ( Physical Review E).
  • Mathematical derivation of the Steady State Evans Searles FT from the Transient Fluctuation Theorem - J. Stat. Phys.
  • Direct verification that time-reversibility is a necessary condition for the Evans Searles Fluctuation Theorem - Pure and Applied Chemistry, Procedings of the 19th IUPAC Conference on Chemical Thermodynamics 2006.
  • Deterministic derivation of the Second Law Inequality from the Jarzynski Relation - C.R. Physique (2007).
  • First experimental confirmation of fluctuation theorems for viscoelastic media (where the white noise Langevin equation fails) - J. Opt. A: Pure Appl. Opt., 9 2007.
  • Studies of certain conjectures regarding far from equilibrium steady state flucuation theorems - when the number of positive and negative Lyapunov exponents become unequal.
  • On Irreversibility, Dissipation and Response Theory.
  • The Relaxation Theorem
  • A simple mathematical proof of Boltzmann's equal a priori probability hypothesis
    Papers on glasses and related topics
  • Statistical Mechanics of Time Independent Non-Dissipative Nonequilibrium States
  • The Glass Transition and the Jarzynski Equality

  • Dissipation and the Foundations of Statistical Thermodynamics
    by Denis J. Evans, Debra J. Searles and Stephen R. Williams

    Statistical Mechanics of NonEquilibrium Liquids

    by Denis J. Evans and Gary P. Morriss

    The second edition of my book with Gary Morriss was published in 2008.
    Publisher: Cambridge University Press; 2 edition
    ISBN-10: 0521857910
    ISBN-13: 978-0521857918

    The first edition was published by Academic Press, London 1990, Theoretical Chemistry Monograph Series.

    The first edition is no longer available from Academic Press. We therefore provide this web version of the book here. The first edition is also available at the Australian National University ePress. The ePress version is available electronically or in a softbound copy for a small fee.

    These files are available for personal use only. No bulk reproduction or resale is permitted. The first edition is Copyright © 1990 Denis J. Evans and Gary P. Morriss.

    A major review which includes a treatment of molecular fluids is given in:

    Sarman S., Evans D.J. and Cummings P.T., "Recent developments in non-Newtonian molecular dynamics", Physics Reports, Elsevier (Ed. M.J. Klein), 305(1-2) 1-92 (1998).

    Statistical Mechanics Links. (People, conferences, organisations)

    Australia hosted Statphys 24, in Cairns Queensland, July 19-23, 2010.

    Links. for students, postdocs and visitors to Canberra.




    If you have comments or suggestions, email me at

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