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

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