Erratum: Virtual double-well potential for an underdamped oscillator created by a feedback loop (J. Stat. Mech. (2022) 053209 DOI: 10.1088/1742-5468/ac6d62)

In this note, we correct the expression of the switching rate of the potential barrier for a system at temperature T expressed in equation (8) and derived in appendix B. We also update below all the equations using the switching rate expression. The error is nevertheless small enough to not change any of the other results or conclusions of the paper. The error came from the assumption that the total energy in the double well potential E was simply distributed according to the Boltzmann probability distribution (Formula Presented) , which would be valid only in an harmonic potential. Indeed, in the double well potential, the motion period depends on the system energy. Therefore the probability distribution of the energy P(E) is obtained by integrating the Boltzmann canonical distribution on the time [−T (E)/2 + T (E)/2 ] range (time range required to explore the full phase space). Contrary to the harmonic case where T (E) = T is constant, here the energy dependence modifies the expression of P(E).