Quantitative analysis of non-equilibrium systems from short-time experimental data

Abstract

We provide a minimal strategy for the quantitative analysis of a large class of non-equilibrium systems in a steady state using the short-time Thermodynamic Uncertainty Relation (TUR). From short-time trajectory data obtained from experiments, we demonstrate how we can simultaneously infer quantitatively, both the thermodynamic force field acting on the system, as well as the exact rate of entropy production. We benchmark this scheme first for an experimental study of a colloidal particle system where exact analytical results are known, before applying it to the case of a colloidal particle in a hydrodynamical flow field, where neither analytical nor numerical results are available. Our scheme hence provides a means, potentially exact for a large class of systems, to get a quantitative estimate of the entropy produced in maintaining a non-equilibrium system in a steady state, directly from experimental data.

Experimental verification of Arcsine laws in mesoscopic non-equilibrium and active systems

“…The flow field skews the symmetry of the position distribution of the trapped particle. In Ref [23], we observe how the flow-field and the current increase when we trap the particle at the close proximity of the bubble. However, in Fig.…”

“…5(c) & (f), we show that the effective spread of x−λ is in tens of nanometers, which increases with increasing amplitude of the added noise. It has been demonstrated in Ref [23] that increase in the entropy production rate or the work dissipated is not infinite but has an upper-bound.…”

“…However, for non-periodic systems that remain in a steady state out of equilibrium, the physics of operation is entirely different, with (∆F = 0). On another note, interest regarding systems driven with colored noise [19,20] has been growing in the scientific community, primarily due to the fact that these serve as a tunable model in understanding real-world biological systems at the microscopic level -especially where phenomena such as non-Gaussian displacement statistics [21], active dissipative fluctuations [22], and flows [23] may become prominent. There is an obvious requirement to study the long-term statistics of stochastic micro-currents that drive these systems in a steady state, since any deviations from the arcsine laws will capture "aging" [15] and "non-markovian" [13] behavior that determine the efficiency of these micro-engines.…”

Non-monotonic skewness of currents in non-equilibrium steady states

“…From the generality of the above arguments, we expect this behaviour to be generic for any non-equilibrium steady state current if the short-time and long-time behaviour are as detailed above. But to be more concrete, we now take the example of the non-equilibrium steady state of a colloidal system [24,35,[46][47][48][49], which can be described by an overdamped diffusive process in 2D. The model consists of a single colloidal particle in a harmonic trap with stiffness κ, whose mean position is modulated according to the Ornstein-Uhlenbeck process.…”

“…It has been shown that Eq. ( 1) saturates for J = ∆S tot in the limit t → 0 for overdamped diffusive processes [32][33][34][35]. As a consequence, σ can be exactly inferred for such systems by studying the mean and variance of current fluctuations at short times [32][33][34][35], even for non-stationary systems [36].…”