Resetting without resetting: An alternate strategy to experimentally verify optimal mean first passage time under...

A simple and broadly applicable a posteriori stochastic resetting protocol that enables the exploration of resetting dynamics without physically performing resets during experiments is proposed. To demonstrate the utility and applicability of the method, we apply it to an autonomous Hexbug robot navigating within a confined rectangular arena with reflecting like boundaries and a single absorbing target (hole). In each trial, the Hexbug starts from a fixed initial position and is allowed to move freely until it reaches the target, marking the first passage time (FPT). This process is repeated for 201 independent realizations to build an empirical distribution of FPTs. Instead of applying resets during the experiments, we implement stochastic resetting a posteriori by applying exponentially distributed resets (i.e., Poissonian resetting) to the recorded FPTs. This strategy allows us to compute the mean first passage time (MFPT) at any reset rate without perturbing the experiments. Moreover, this method generates a new set of FPTs every time the algorithm is implemented. This enables one to render a theoretically infinite amount of data from a small experimental dataset. Our results reveal a clear nonmonotonic dependence of the MFPT on the reset rate, with a distinct minimum, a hallmark signature of optimal resetting. Furthermore, the data generated by the algorithm also obey Reuveni universality. This strategy can be indispensable in setups in which physical resetting is not feasible. It circumvents the challenges of repeated experimental resets, offering an accessible platform to investigate optimization strategies and/or first passage phenomena.