The accumulation phenomenon commonly occurs in fluvial processes. Accurately considering the accumulation effects of previous water and sediment conditions is essential for the study of riverbed evolution. To reveal the physical dynamics of the accumulation phenomenon, herein various geometry observations upstream and downstream of dam on several domestic and overseas typical fluvial rivers were analyzed. To do this, the changes in water and sediment conditions were defined as external disturbances, based on assumptions that the probability of an external disturbance conforms to the Poisson distribution and the feedback intensity induced by an individual disturbance decays exponentially with time. In this paper, a mathematical description of the accumulation processes of internal feedback induced by external disturbances is given, and a corresponding theoretical model is proposed for simulating the spatio-temporal adjustment processes of river characteristic variables on the basis of the stochastic theory in statistical mechanics. Further, the above models were then applied to investigate the spatio-temporal adjustment processes of the upper and lower reaches of dams after their construction. Results revealed two key findings. (i) Temporally, the vertical, lateral, and whole reaches' adjustment rates over time are relatively fast in the early period following disturbances but then slow down rapidly, while the accumulated bed degradation, river width and accumulated sedimentation continuously increase until a new dynamic equilibrium state is attained; these phenomena reflect the representative accumulation characteristics of fluvial processes. (ii) Spatially, the erosion intensity downstream of dams decreases nonlinearly along the channel until it eventually diminishes. In fact, the unbalanced distribution of erosion intensity across space arises from the system feedback caused by external disturbances propagating in space yet decaying over time, which is another external manifestation of an accumulation characteristic in fluvial processes. Model applications indicate that the spatio-temporal adjustment processes of cross sections and channel reaches can be accurately described by the unified theoretical formula derived from equation deforming, since the model predictions show good agreement with observed field data: coefficient of determination (R²) between them attained values of 0.92, 0.93, 0.76, and 0.95. The proposed theoretical models take both the accumulative characteristics of fluvial processes and the spatial propagation characteristics of system feedback into account synthetically. In demonstrating this approach, this study provides the theoretical basis and new calculation method for quantitatively describing the spatio-temporal adjustment processes of non-equilibrium fluvial channels following disturbances.