Arbitrarily slow, non-quasistatic, isothermal transformations

TL;DR

This study demonstrates that in overdamped colloidal systems, arbitrarily slow isothermal transformations can be non-reversible, with work requirements depending on the transformation protocol, challenging traditional assumptions about reversibility at slow speeds.

Contribution

It reveals that slow, smooth, isothermal transformations in colloidal particles can be non-reversible, and shows how protocol order affects work and reversibility, supported by a new theoretical formula.

Findings

One protocol requires no work at slow speeds.

Another protocol requires finite work regardless of slowness.

Work differences are linked to protocol reversal and relative entropy.

Abstract

For an overdamped colloidal particle diffusing in a fluid in a controllable, virtual potential, we show that arbitrarily slow transformations, produced by smooth deformations of a double-well potential, need not be reversible. The arbitrarily slow transformations do need to be fast compared to the barrier crossing time, but that time can be extremely long. We consider two types of cyclic, isothermal transformations of a double-well potential. Both start and end in the same equilibrium state, and both use the same basic operations---but in different order. By measuring the work for finite cycle times and extrapolating to infinite times, we found that one transformation required no work, while the other required a finite amount of work, no matter how slowly it was carried out. The difference traces back to the observation that when time is reversed, the two protocols have different outcomes, when carried out arbitrarily slowly. A recently derived formula relating work production to the relative entropy of forward and backward path probabilities predicts the observed work average.