Counting translocations of strongly repelling particles through single channels: Fluctuation theorem for membrane transport

Transport of strongly repelling particles through a single membrane channel is analyzed assuming that the channel cannot be occupied by more than one particle. An exact solution is found for the Laplace transform of the probability P(n)(t) that n particles have been transported in time t. This transform is used to find the flux through the channel and to show that P(n)(t) and P(-n)(t) are related by the fluctuation theorem. The solution is obtained using an observation that P(n)(t) is the propagator for a non-Markovian random walk, which can be found by solving a set of integral equations.