  We analyze the thermodynamic cost of a logically reversible Brownian Turing
machine operating in the first-passage time protocol based on the stochastic
thermodynamics of resetting. In this framework, the thermodynamic cost of
computation is the reset entropy production, which is interpreted as the
information reduction by a resetter external to the computer. At the level of a
single trajectory, the reset entropy production is associated with
unidirectional transitions and is a function of the time-dependent distribution
probability. We analyze an approximation that replaces the distribution
probability with the empirical sojourn time, which can be obtained at the
single-trajectory level. The approximation is suitable for the numerical
analysis by the Gillespie algorithm and provides a reasonable average value for
the reset entropy.

Statistical Mechanics