Tribo-films form on surfaces as a result of friction and wear. The wear rate is dependent on the frictional processes, which develop within these tribo-films. Physical–chemical processes with negative entropy production enhance reduction in the wear rate. Such processes intensively develop once self-organization with dissipative structure formation is initiated. This process leads to significant wear rate reduction. Self-organization can only occur after the system loses thermodynamic stability. This article investigates the behavior of entropy production that results in the loss of thermodynamic stability in order to establish the prevalence of friction modes required for self-organization. Tribo-films with dissipative structures form on the friction surface as a consequence of a self-organization process, resulting in an overall wear rate reduction. It has been demonstrated that a tribo-system begins to lose its thermodynamic stability once it reaches the point of maximum entropy production during the running-in stage.