Arbitrarily Slow, Non-quasistatic, Isothermal Transformations

Abstract

Joule or free expansion of an ideal gas into a volume with a lower pressure is an example of an irreversible isothermal process. This nonequilibrium example is often used in traditional thermodynamics text books to demonstrate that an arbitrarily slow process need not be reversible. Cyclic operation of any engine that involves a free expansion is therefore necessary dissipative. Here, we explore experimentally the origin of the thermodynamic irreversibility at the level of a single-particle gas. A feedback trap is used to confine a silica particle in a virtual bistable potential, creating a system analogous to two vessels connected by a valve, where volume of one vessel is adjustable via piston. We operate two types of cyclic transformations, both start and end in the same equilibrium state, and both use the same basic operations—but in different order. One transformation required no work, while the other required work, no matter how slowly it was carried out. A statistical analysis and a recently derived formula are used to show that the difference traces back to the observation that when time is reversed the two protocols have different outcomes. This property is not possible to notice in a single repetition, unlike in a macroscopic system where free expansion is followed by a “whoosh”.