Apparent violations of the second law in two-level systems

Probabilistic Work Extraction on a Classical Oscillator Beyond the Second Law

We demonstrate experimentally that, applying optimal protocols that drive the system between two equilibrium states characterized by a free energy difference ΔF, we can maximize the probability of performing the transition between the two states with a work W smaller than ΔF. The second law holds only on average, resulting in the inequality ⟨W⟩≥ΔF. The experiment is performed using an underdamped oscillator evolving in a double-well potential. We show that with a suitable choice of parameters the probability of obtaining trajectories with W≤ΔF can be larger than 95%. Very fast protocols are a key feature to obtain these results, which are explained in terms of the Jarzynski equality.

Detailed fluctuation theorem bound for apparent violations of the second law

The second law of thermodynamics is a statement about the statistics of the entropy production, 〈Σ〉≥0. For small systems, it is known that the entropy production is a random variable and negative values (Σ<0) might be observed in some experiments. This situation is sometimes called apparent violation of the second law. In this sense, how often is the second law violated? For a given average 〈Σ〉, we show that the strong detailed fluctuation theorem implies a lower tight bound for the apparent violations of the second law. As applications, we verify that the bound is satisfied for the entropy produced in the heat exchange problem between two reservoirs mediated by a bosonic mode in the weak-coupling approximation, a levitated nanoparticle, and a classical particle in a box.