Beating Landauer's bound by Memory Erasure using Time Multiplexed Potentials

The Landauer's Principle, proposed by Rolf Landauer in 1961, states that the logically irreversible operation of erasing a single bit of information requires atleast k_bT ln 2 amount of energy, k_b and T being Boltzmann's constant and temperature respectively. However, Landauer's bound holds only for erasure mechanisms that are perfect. In this article we investigate the effect of imperfections in erasure mechanisms. If the proportion of successful erasures is quantified by p, we show that the minimum energy needed to erase a bit of information is given by k_bT[ln 2 + p ln p + (1 - p) ln (1 - p)], also known as the Generalized Landauer bound. Furthermore, we provide a mechanism for realizing a memory bit by multiplexing an optical trap rapidly and propose a mechanism of erasure, for various success proportions p. Using our framework, we show using Monte Carlo simulations that heat dissipation lower than the Landauer's bound is achievable by reducing p. Thus, we establish an independent method of beating Landauer's bound by resorting to partially successful erasures.