A Cost/ Speed/ Reliability Trade-off in Erasing a Bit

We present a novel treatment of the fundamental problem of erasing a bit. We propose a cost function that extends to path space the principle due to Szilard and Landauer that erasing a bit requires at least kBT log 2 units of energy. We introduce notions of reliability of information storage via a reliability timescale τr, and speed of erasing via an erasing timescale τe. Our problem formulation captures the tradeoff between speed, reliability, and the action required to erase a bit. We show that erasing a reliable bit fast costs at least log 2 − 1 2 log ( 1 − e−2τe/τr ) > log 2 units, which goes to 1 2 log 2τr τe units when τr >> τe.