After the concept of entropy has been introduced in the classical approach to thermodynamics, the definition of a reversible process may be refined in a mathematical way. If a given process can be modified by appropriate adjustment of the thermodynamic force involved so that it approaches a limit of zero entropy production, defining a limit process, and if the reverse process can be similarly modified, defining the same limit process in reverse, then we say that the process is reversible in this limit. Two examples are given, one dealing with the heating of a system and the second involving the adiabatic expansion of a viscous ideal gas.