In the Carnot cycle, the ratio of the heat exchanged during the two reversible and isothermal processes and the temperatures of the isotherms are the same. Since the other two processes are reversible and adiabatic, there is no heat exchange. Hence, the net entropy change in the cycle, the sum of the entropy change for all the processes, is zero. Any reversible, cyclic process can be shown to be a sum of many Carnot cycles. Thus, the net entropy change during the process is zero. Take an arbitrary, closed path for a reversible cycle and break it into two parts, I and II, operating between the points A and B. Split the cyclic integral of entropy into two parts along I and II. Since the process is reversible, reverse the integral for path II. Thus, it is found that the entropy change between any two points along two independent paths is the same. Hence, entropy is a state function, similar to internal energy.