Fast is hot: energetics of information erasure and the overhead to Landauer's bound at low dissipation*

Information processing in the physical world comes with an energetic cost: Landauer's principle states that erasing a 1-bit memory requires at least kBT0 ln 2 of energy, with kBT0 the thermal energy of the surrounding bath. Practical erasures implementations require an overhead to Landauer's bound, observed to scale as kBT0 B/t, with t the protocol duration and B close to the system relaxation time. Most experiments use overdamped systems, for which minimizing the overhead means minimizing the dissipation. Underdamped systems, never harnessed before, thus sounds appealing to reduce this energetic cost. 

We use as one-bit memory an underdamped micro-mechanical oscillator confined in a double-well potential created by a feedback loop. The potential barrier is precisely tunable in the few kBT0 range. Within the stochastic thermodynamic framework, we measure both the work and the heat of the erasure protocol. We demonstrate experimentally and theoretically that Landauer's bound can be saturated (within a 1% uncertainty) with quasi-static protocols.

Furthermore, we show that for such underdamped systems, fast erasures induce a heating of the memory: the work influx is not instantaneously compensated by the inefficient heat transfert to the thermostat. This temperature rise results in a kinetic energy cost superseding the viscous dissipation term. Our model covering all damping regimes paves the way to new optimisation strategies in information processing, based on the thorough understanding of the energy exchanges. We are indeed able to quantify the overhead to Landauer's bound with its dependence on the system and protocol parameters, and we identify the physical origins of this energy cost.