The Landauer principle states that at least k_BTln2 of energy is required to erase a 1-bit memory, with k_BT the thermal energy of the system. Practical erasure implementations re- quire an overhead to Landauer’s Bound (LB), observed to scale as k_BT × B/τ, with τ the protocol duration and B close to the system relaxation time. Most model experiments use overdamped systems, for which minimizing the overhead means minimizing the dissipation. Underdamped systems thus sound appealing to reduce this energetic cost, and are the object of this presentation. Our experiment implements a model 1-bit memory based on a micro-mechanical oscillator confined in a double-well potential created by a feedback loop [1]. We measure the work and the heat of informa- tion processing protocols within the stochastic thermodynamic framework. Our research covers all possible operations on a single bit b: HOLD (b → b), SET (b → 0 or 1), NOT (b → ¬b).
 
The logical SET operation is an erasure, logically irreversible, coming with an entropic cost which is at least LB. We demonstrate that, in our experiment, this bound is reached with a 1% uncertainty, with protocols as short as 100 ms [2]. Besides, we show experimentally and theoretically that for underdamped systems, fast erasures induce a heating of the memory: the work influx is not instantaneously compensated by the inefficient heat transfer to the thermostat. This temperature rise results in a kinetic and potential energy contribution superseding the viscous dissipation term. Our model covering all damping regimes paves the way to new optimization strategies in information processing [3, 4], including the implementation of more applied logic gates performing repeated fast operations [6].
 
The other logical operations are reversible, and can thus in principle be performed at no ther- modynamical cost. We implement the NOT operation using the momentum degree of freedom in our underdamped memory to perform a bit-flip [5]. Not bounded by any entropic cost this time, the energetic cost of the protocol vanishes as the quality factor of the oscillator increases, further highlighting the low energy footprint and interest of underdamped memories.