Electrolysis and Thermodynamics
During electrolysis, the amount of electrical energy that must be added equals the change in Gibbs free energy of the reaction plus the losses in the system. The losses can (theoretically) be arbitrarily close to zero, so the maximum thermodynamic efficiency of any electrochemical process equals 100%. In practice, the efficiency is given by electrical work achieved divided by the Gibbs free energy change of the reaction.
In most cases, such as room temperature water electrolysis, the electric input is larger than the enthalpy change of the reaction, so some energy is released as waste heat. In the case of electrolysis of steam into hydrogen and oxygen at high temperature, the opposite is true. Heat is absorbed from the surroundings, and the heating value of the produced hydrogen is higher than the electric input. In this case the efficiency relative to electric energy input can be said to be greater than 100%. The maximum theoretical efficiency of a fuel cell is the inverse of that of electrolysis. It is thus impossible to create a perpetual motion machine by combining the two processes.
Read more about this topic: High-temperature Electrolysis