Integrated Calendar

As famously articulated by Sir Arthur Eddington, the second law of thermodynamics implies a directionality to the flow of time: the arrow of time points in the direction of increasing entropy. This observation is something that we understand intuitively in our everyday lives, but with nanoscale systems the situation becomes subtle due to the prominence of statistical fluctuations. At sufficiently small length and time scales, a system may behave in a manner that appears contrary to the second law. Surprisingly, our ability to distinguish the direction of the arrow of time can be quantified and shown to obey a universal law, which holds for both small and large systems. I will show how this law emerges from non-equilibrium fluctuation relations, and I will present experimental results that have verified its validity, using a driven quantum dot.

I will also discuss so-called "violations" of the second law. For isothermal processes, these violations occur when W < Delta F, where W is the work performed on the system and Delta F is the free energy change. A natural measure of the magnitude of the violation is given by the dimensionless quantity x = (Delta F - W)/kT. I will derive a simple expression that provides a bound on the probability of observing such violations, as a function of x, and I will argue that this expression provides the tightest possible universal bound. Quantum dots may provide experimental illustrations of the saturation of this bound.