Ions flowing independently in an ensemble of narrow, multisite channels under a constant chemical or electrochemical potential reach;a stationary state distribution that is maintained by the steady dissipation of the driven system. This distribution and the total ion population in an ensemble of channels are proportional to the ratio of the Injection flux j and the eigenvalues for the multistate system. The macroscopic flux and dissipation, determined by the bathing solution concentrations and potentials, dictate relationships between the forward and reverse transition probabilities in the channel; The character of the stationary state distribution is defined with "thermodynamic" parameters analogous to equilibrium thermodynamic quantities using injection fluxes and transition probabilities. The stationary state distributions generated for these self consistent conditions include the equilibrium Boltzmann distributions as special cases, i.e., in the limit of zero net flux through the channels. Various aspects of the model can be tested using both laser Doppler velocimetry and electrochemical measurements.