We suggest employing log-ergodic processes to simulate the velocity of money in an ergodic manner. Our approach sheds light on economic behavior, policy implications, and financial dynamics by maintaining long-term stability. By bridging theory and practice, the partially ergodic model helps analysts and policymakers comprehend and forecast velocity of money. The empirical analysis, using historical U.S. GDP and money supply data, demonstrates the model's effectiveness in capturing the long-term stability of the velocity of money. Key findings indicate that the log-ergodic model offers superior predictive power compared to traditional models, making it a valuable tool for policymakers to control economic factors in vital situations.