An optical trap experiment to demonstrate fluctuation theorems in viscoelastic media

Abstract

Conventional 19th century thermodynamics has limited our understanding of statistical physics to systems in the thermodynamic limit, at or near equilibrium. However, in the last decade two new theorems, collectively referred to as fluctuation theorems or FTs, were introduced that quantify the energy distributions of small systems that are driven out of equilibrium, possibly far from equilibrium, by an external field. As such the FTs represent a much needed extension of non-equilibrium thermodynamics that can potentially address systems of interest in the 21st century, including nano/micro-machines and single biomolecular function. Optical trapping has served as an ideal experimental technique for demonstrating these theorems. Measurement of picoNewton scale forces over nanometre-sized displacements of a trapped micron-sized particle allows us to measure the energies to a fraction of thermal energy along the particle's trajectory—precisely what is needed to demonstrate the predictions of the FTs. Here we review the fluctuation theorems, as cast by Evans and Searles (1994 Phys. Rev. E 50 1645; 2002 Adv. Phys. 51 1529; 2004 Aust. J. Chem. 57 1119) and Crooks (1999 Phys. Rev. E 60 2721), and provide a discussion of their importance and a comparison of their arguments. We further demonstrate an optical trap experiment that confirms the FTs. We have chosen to review an optical trapping experiment that is identical to a previously published experiment (Carberry et al 2004 Phys. Rev. Lett. 92 140601), but where the solvent is viscoelastic rather than purely viscous. This represents the first experimental demonstration where dynamics of the colloidal particle are complex and not known a priori.