Reversible means we can run the process reverse way without any "strangeness". Reverse the process means turn all the interactions opposite way. Lets say, in some process, you transferred out of the system 10 kJ of heat (sign of heat transferred out of the system is negative so Q=-10 kJ). Reverse the process is to transfer this 10kJ back to system from surroundings (positive sign this time). Now, let say, the system is actually hotter than surrounding, so you transfer out this 10 kJ of heat easily (if the system has large heat capcity we can neglect the fact that it cooled slightly). But going back is a little awkward, system is still hotter and we want to "put heat" back to the system. Its just impossible. But what is potentially possible is to transfer heat back and forth (avoiding any strangeness) without any temperature difference (or infinitesimally small temperature difference - so how small is really infinitesimally small?). My conclusion is that reversible processes are potentially attainable but not realistic (something like perfect beauty) - every real process is indeed irreversible. Yet we use it in thermodynamics as simplification of real processes, and we can obtain realtively simple mathematical equations for them. So essentially discussion about realism of reversible processes are something like discussion about realism of point concept in geometry.

Reversible means we can run the process reverse way without any "strangeness". Reverse the process means turn all the interactions opposite way. Lets say, in some process, you transferred out of the system 10 kJ of heat (sign of heat transferred out of the system is negative so Q=-10 kJ). Reverse the process is to transfer this 10kJ back to system from surroundings (positive sign this time). 

Now, let say, the system is actually hotter than surrounding, so you transfer out this 10 kJ of heat easily (if the system has large heat capacity we can neglect the fact that it cooled slightly). But going back is a little awkward, system is still hotter and we want to "put heat" back to the system. Its just impossible. But what is potentially possible is to transfer heat back and forth (avoiding any strangeness) without any temperature difference (or infinitesimally small temperature difference - so how small is really infinitesimally small?). 

My conclusion is that reversible processes are potentially attainable but not realistic (something like perfect beauty) - every real process is indeed irreversible. Yet we use it in thermodynamics as simplification of real processes, and we can obtain relatively simple mathematical equations for them. 

So essentially, the discussion about realism of reversible processes are something like discussion about realism of point concept in geometry.