A key function of the brain is to process noisy sensory stimuli to make fast and accurate decisions. Canonical studies manipulate average noise to study stimulus effects on decision parameters, but how processing of exact stochastic fluctuations impacts the decision outcome, has remained largely unexplored. We conducted behavioral experiments with stimuli following physical motion equations under nonequilibrium processes to define the stimulus dynamics in detail. In experiment I, participants (N=21) judged the motion direction of a visual stimulus with a given drift velocity (v) and diffusion (D) coefficient. We controlled v and D to manipulate the rate of entropy production emerging from the stimulus trajectory as a measure of noise. Using an analytical model equivalent to a Drift Diffusion Model, we predicted optimal decision times. Results revealed: (1) an inverse relationship between mean decision time and entropy production rate, consistent with model predictions; however, we also observed (2) trial-by-trial variability in decision thresholds, and (3) slower decision times compared to model predictions. We hypothesized that the lack of leaky memory in this model could be the reason for these discrepancies. We developed an evidence integration model where evidence is exponentially weighted based on stimulus position, separating noise dynamics in the integrator’s memory from momentary evidence. Analyses suggested: (1) increased entropy production enhances recent information retention in memory while reducing the weight of momentary evidence, (2) implementing adaptive leaky memory improved trial-by-trial predictions in decision times, and thresholds. In experiment II (N=24), we varied v and D combinations to characterize the decision patterns in a larger parameter space. Results showed (1) the predictability of the models was generalizable across parameter space. Moreover, decision times were driven by D, and accuracy by the v-to-D ratio. (2) Comparing identical conditions between experiments I and II, we found that having randomized conditions within blocks in the latter prevented adaptation to stimulus statistics, leading to suboptimal behavior, such as longer decision times, larger decision thresholds, and lower accuracy. Overall, our studies show that leveraging the controlled fluctuations of stimuli allows us to better characterize variables influencing decisions and refines our understanding of efficient evidence integration under uncertainty.