Experimental Test of Hatano and Sasa's Nonequilibrium Steady-State Equality

Most natural processes occur far from equilibrium and cannot be treated within the framework of classical thermodynamics. In 1998, Oono and Paniconi [Oono, Y. & Paniconi, M. (1998) Prog. Theor. Phys. Suppl. 130, 29-44] proposed a general phenomenological framework, steady-state thermodynamics, encompassing nonequilibrium steady states and transitions between such states. In 2001, Hatano and Sasa [Hatano, T. & Sasa, S. (2001) Phys. Rev. Lett. 86, 3463-3466] derived a testable prediction of this theory. Specifically, they were able to show that the exponential average of Y, a quantity similar to a dissipated work, should be equal to zero for arbitrary transitions between nonequilibrium steady states, $-{\rm ln}\langle e^{-Y}\rangle =0$. We have tested this strong prediction by measuring the dissipation and fluctuations of microspheres optically driven through water. We have found that $-{\rm ln}\langle e^{-Y}\rangle \approx 0$ for three different nonequilibrium systems, supporting Hatano and Sasa's proposed extension of thermodynamics to arbitrary steady states and irreversible transitions.