Demonstration of the steady-state fluctuation theorem from a single trajectory

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The fluctuation theorem (FT) quantifies the probability of Second Law of Thermodynamicsviolations in small systems over short timescales. While this theorem has beenexperimentally demonstrated for systems that are perturbed from an initial equilibriumstate, there are a number of studies suggesting that the theorem applies asymptotically inthe long time limit to systems in a non-equilibrium steady state. The asymptoticapplication of the FT to such non-equilibrium steady-states has been referred to in theliterature as the steady-state fluctuation theorem (or SSFT). In 2005 Wang et al demonstrated experimentally an integrated form of the SSFT using a colloidal bead thatwas weakly held in a circularly translating optical trap. Moreover, they showed that theintegrated form of the FT may, for certain systems, hold under non-equilibrium steadystates for all time, and not just in the long time limit, as suggested by the SSFT. Whiledemonstration of the integrated forms of these theorems is compact and illustrative, aproper demonstration shows the theorem directly, rather than in its integrated form. Inthis paper, we present experimental results that demonstrate the SSFT directly,and show that the FT can hold for all time under non-equilibrium steady states.