But an exact theorem exists, relating to the statistics of motion in flowing systems. It governs the steady state motion of any sheared fluid that is stochastic (subject to thermal noise from its environment), ergodic (sufficiently mobile to thoroughly explore its space of available states) and microscopically reversible (contains normal particles with no sense of direction; this does not apply, for instance, to traffic flow).
The new theorem embodies a set of rules that put constraints on the modelling of non-equilibrium systems, ensuring self-consistency and no unwarranted bias. The resulting mathematical structure bears beautiful similarities to that of equilibrium statistical mechanics, and has as much potential for diverse and important applications. I believe that this development will shift the paradigm for theoretical modelling of non-equilibrium systems, removing the arbitrariness from the subject, and providing a foundation of rigorous statistical arguments. Potentially, the formalism should be able to explain much of the phase behaviour of fluids under flow.
This development has been timely, as there is rapidly increasing interest in exact non-equilibrium statistical mechanics, following a number of other recent exact theorems: "Fluctuation Theorems" have been discovered, quantifying the probability of momentary violations of the second law of thermodynamics, and "Non-equilibrium Work Theorems" have provided some exact criteria for the work done by non-equilibrium changes to the constraints on a thermodynamic system (with implications e.g. for experiments on forced unfolding of proteins). Also, the Lee-Yang theory of phase transitions has been generalised to a large class of non-equilibrium models. ( Richard Blythe is one of the authors of that work.) The subject area of non-equilibrium steady states now has huge potential for important discoveries.
My aim is now to explore the implications of the new theorems, by constructing simplified models, as well as making calculations for real systems (such as polymers under flow) that can be tested experimentally.
Click to hear an Isaac Newton Institute seminar on my research intonon-equilibrium steady states of matter.
(For a full list, click here.)
Statistical mechanics far from equilibrium: Prediction and test for a sheared system
R M L Evans, R A Simha, A Baule and P D Olmsted,
Phys. Rev. E 81, 051109 (2010).
Direct conversion of rheological compliance measurements into storage and loss moduli
R M L Evans, Manlio Tassieri, Dietmar Auhl, and Thomas A. Waigh,
Phys. Rev. E 80, 012501 (2009).
Invariant quantities in shear flow
A Baule and R M L Evans,
Phys. Rev. Lett. 101, 240601 (2008).
Dynamics of Semiflexible Polymer Solutions in the Highly Entangled Regime
Manlio Tassieri, R. M. L. Evans, Lucian Barbu-Tudoran, G. Nasir Khaname, John Trinick, and Tom A. Waigh,
Phys. Rev. Lett. 101, 198301 (2008).
Rules for transition rates in nonequilibrium steady states ,
R M L Evans,
Phys. Rev. Lett. 92, 150601 (2004).
Universal law of fractionation for slightly polydisperse systems
R M L Evans, D J Fairhurst and W C K Poon,
Phys. Rev. Lett. 81, 1326-1329 (1998).
Colloid-polymer mixtures at triple coexistence: Kinetic maps from free-energy landscapes,
W C K Poon, F Renth, R M L Evans, D J Fairhurst, M E Cates and P N Pusey,
Phys. Rev. Lett. 83, 1239-1242 (1999).
Correlation length by measuring empty space in simulated aggregates,
R M L Evans and M D Haw,
Europhys. Lett. 60(3), 404-410 (2002).
Role of metastable states in phase ordering dynamics,
R M L Evans, W C K Poon and M E Cates,
Europhys. Lett. 38, 595-600 (1997).
Detailed balance has a counterpart in non-equilibrium steady states,
R M L Evans,
J. Phys. A: Math. Gen. 38, 293-313 (2005).
A theoretical study of orientational order in liquid crystal vesicles,
R. M. L. Evans,
University of Manchester Thesis (1995).
For a full list of publications, click here.