The Landauer principle sets a fundamental thermodynamic constraint on the
minimum amount of heat that must be dissipated to erase one logical bit of
information through a quasi-statically slow protocol. For finite time
information erasure, the thermodynamic costs depend on the specific physical
realization of the logical memory and how the information is erased. Here we
treat the problem within the paradigm of a Brownian particle in a symmetric
double-well potential. The two minima represent the two values of a logical
bit, 0 and 1, and the particle’s position is the current state of the memory.
The erasure protocol is realized by applying an external time-dependent tilting
force. Combining probabilistic survival analysis with instanton calculus, we
derive analytical tools to evaluate the work required to erase a classical bit
of information in finite time via an arbitrary continuous erasure protocol,
which is a relevant setting for practical applications. Importantly, our method
is not restricted to the average work, but instead gives access to the full
work distribution arising from many independent realizations of the erasure
process. Using the common example of an erasure protocol that changes linearly
with time, we explicitly calculate all relevant quantities and verify them
numerically.
