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Nonequilibrium statistical mechanics and dynamical systems, New ideas and techniques from the modern theories of chaotic dynamical systems suggest that a new fundamental conceptual basis for a theory of nonequilibrium steady states is possible. We have proved the conjugate pairing rule for a class of thermostatted nonequilibrium steady states and together with Evans and Cohen established the fluctuation theorem.

Probing the hyperbolicity of high dimensional systems at equilibrium and nonequilibrium by calculating the instantaneous stable and unstable manifolds using covariant Lyapunov vectors has given a rich understanding of system behaviour.

Current projects include heat conduction in quasi-one-dimensional systems and nonequilibrium entropy.