Irreversibility to Reversibility Crossover in Transient Response of an Optically Trapped Particle

We study the transient response of a colloidal bead which is released from different heights and allowed to relax in the potential well of an optical trap. Depending on the initial potential energy, the system’s time evolution shows dramatically different behaviors. Starting from the short-time reversible to long-time irreversible transition, a stationary reversible state with zero net dissipation can be achieved as the release point energy is decreased. If the system starts with even lower energy, it progressively extracts useful work from thermal noise and exhibits an anomalous irreversibility. In addition, we have verified the Transient Fluctuation Theorem and the Integrated Transient Fluctuation Theorem even for the non-ergodic descriptions of our system. Since the origin of the second law of thermodynamics which defined a direction of time, a question is often asked: how the irreversible property emerges from the reversible dynamics at microscopic scales [1]. A detailed examination of the problem reveals that the mystery lies in its spontaneous energy dispersal as dissipation. It makes us curious about the time evolution of small stochastic systems where the thermal fluctuations become comparable to the dissipative loss. It is only in the last decade that this interesting issue has been addressed in terms of the Fluctuation Theorems [2–5]. Evans and Searles Fluctuation Theorem (FT) [2] gave a quantitative description of irreversibility, providing an analytical expression for the probability of the system trajectories that are associated with a negative dissipative flux. As expected, those ‘antitrajectories’ become visible only for short time scales in microscopic systems. Laboratory experiments with biomolecules manipulated mechanically [6,7] or colloidal particles in optical trap [8–14] have been reported subsequently corroborating the theorem(s). In this Letter we address this important issue of reversibility with a closer focus on its main controlling factor, the initial potential energy of the system. We show experimentally how a system’s initial energy in comparison to the background thermal noise, entirely dictates its time evolution. Starting with very low energy, the system can even continue to convert the heat fluctuations into useful work as it evolves in time. In particular, we have studied the transient response and the reversible behavior of a colloidal bead in a harmonic potential well created by a very weak optical trap. As the bead is released from different points in the potential well landscape with varying initial energy and allowed to equilibrate, the time evolution and the reversibility of the system show a dramatic change in their behavior. If particle starts with a potential energy higher than the average thermal energy of the bath, its mean motion is downhill but the underlying reversibility of the dynamics generates occasional uphill motions. However, with the release point going down the potential well, the reversibility i.e. the probability of performing along the backward direction increases accompanied by a diminished dissipation. At some point, it becomes completely reversible when the forward and backward motions occur with equal probability. If the bead is released from a point which is further down the potential well, the heat flux starts flowing along the opposite direction prevailing the dissipative loss and pushes the system to a higher energy state making the system irreversible again, in the converse direction. These exceptional energy-gaining motions are ultimately a consequence of the micro-reversibility of the system. The results presented in this Letter demonstrate experimentally the competition between micro-reversibility and irreversible dissipation in governing the long-time reversibility of a system. In our study, we have evaluated the dissipation function,