Waiting Time for Transient Violations of the Second Law in Brownian Oscillators

In this work, we study the average time a Brownian oscillator coupled to a thermal bath takes to get fluctuations of a given energy. The waiting times are obtained as a function of the system parameters using the Langevin equation and molecular simulations. We found that an oscillators system can exhibit arbitrarily large transient violations of the second law. It is shown that the waiting times give relevant information that is not provided by the solutions of the Fokker–Planck equation.