Nonequilibrium Fluctuations for a Single-Particle Analog of Gas in a Soft Wall

Abstract

We investigate the motion of a colloidal particle driven out of equilibrium by a time-varying stiffness of the optical trap that produces persistent nonequilibrium work. Measurements of work production for repeated cycles composed of the compression and expansion processes for the optical potential show huge fluctuations due to thermal motion. Using a precise technique to modulate the stiffness in time, we accurately estimate the probability distributions of work produced for the compression and expansion processes. We confirm the fluctuation theorem from the ratio of the two distributions. We also show that the average values of work for the two processes comply with the Jarzynski equality. This system has an analogy with a gas in a breathing soft wall. We discuss about its applicability to a heat engine and an information engine operated by feedback control. The fluctuation theorem for entropy production in a heat bath was discovered for a deterministic dynamics in the early 1990s [1,2]. Later it was also proved theoretically in a wide class of stochastic systems and extended to other thermodynamic quantities such as work and heat [3][4][5][6][7][8].Since it deals with the stochastic distribution for the fluctuation of a thermodynamic quantity, small systems with large fluctuations have been of interest in experimental studies. The first experiment and the following were done for a colloidal particle driven out of equilibrium by moving the center of the trap [9,10], which is regarded as a prototype of nonequilibrium process driven by an external field. Similar experimental systems were studied, such as a molecule in the atomic force microscopy or a colloidal particle in the optical trap pulled by an external force [11], an electrical dipole driven by a small current [12], and a harmonic oscillator under an external force [13,14]. These systems are well described by the overdamped Langevin equation, and theoretical works were accompanied or performed separately [15,16]. There were also experimental studies for biological systems with unknown dynamical details, such as an RNA molecule unfolded and refolded by optical tweezers [17,18] and a rotating motor protein F 1 -ATPase [19], for which agreement with theory is less accurate.In this Letter, we consider the motion of a colloidal particle in an optical trap with a time-varying stiffness. It is characterized by a different nonequilibrium prototype where a protocol changes the shape of potential in time. The theoretical approach is more difficult than that for nonequilibrium driven by an external field [9][10][11][12][13][14], and the probability distribution for the work production is not known rigorously. However, there have been recent theoretical works [20,21] where the moments of the work distribution are obtained. On the other hand, no experimental study on nonequilibrium fluctuations for this system has been done to date, partly due to difficulty in modulating the stiffness accurately. In this work, we use a liquid crystal device to control the stiffness p...

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