Thermodynamic cost of Brownian computers in the stochastic thermodynamics of resetting

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.