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Conventional 19th century thermodynamics have limited our understanding of statistical physics to systems in the thermodynamic limit, at or near equilibrium. In the last decade two new theorems, referred to as the Fluctuation Theorems (FTs), were introduced to quantify the energy distributions of small systems that are driven out of equilibrium, possibly far from equilibrium, by an external field. The FTs represent a much-needed extension of non-equilibrium thermodynamics that can potentially address systems of interest, including nano/micro-machines and single biomolecular function. The first and original FT of Evans et al is a generalisation of the second law of thermodynamics to small systems over short timescales (Denis Evans Research Group), whilst the FT of Crooks, or the Jarzysnki equality, describes the evolution of systems between equilibrium states. In 2002 we demonstrated experimentally, for the first time, the FTs by analysing the trajectories of an isolated colloidal particle in a translating optical trap. However, the motion of a single colloidal particle in a purely viscous solvent is accurately described by the stochastic, inertialess Langevin equation, and as the FTs can also be derived using this same equation of motion with uncorrelated Gaussian noise, one might argue that we merely tested the applicability of the stochastic equation of motion. In 2006 we confirmed the FT using an optically trapped bead in a viscoelastic solvent, for which the stochastic equations of motion require a dissipative term with memory and from which the FTs cannot be derived. This experimental demonstration is a confirmation of the FTs rather than a confirmation of the dynamics that satisfy the FTs. The paper describing the work was singled out and advertised by Institute of Physics editors for its “novelty, signficance and potential impact on future research”. In 2006-07, we wrote a review of the FTs for Annual Reviews of Physical Chemistry using a new notation that emphasises the general applicability of the FTs to small dynamical systems, which are perturbed by a field that acts dissipatively and/or conservatively.
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