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

The fluctuation theorem (FT) quantifies the probability of Second Law of Thermodynamics violations in small systems over short timescales. While this theorem has been experimentally demonstrated for systems that are perturbed from an initial equilibrium state, there are a number of studies suggesting that the theorem applies asymptotically in the long time limit to systems in a non-equilibrium steady state. The asymptotic application of the FT to such non-equilibrium steady-states has been referred to in the literature 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 that was weakly held in a circularly translating optical trap. Moreover, they showed that the integrated form of the FT may, for certain systems, hold under non-equilibrium steady states for all time, and not just in the long time limit, as suggested by the SSFT. While demonstration of the integrated forms of these theorems is compact and illustrative, a proper demonstration shows the theorem directly, rather than in its integrated form. In this 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.