Entropy

If two systems with entropy S₁ and S₂, respectively, are brought into contact with each other, their combined entropy equals S₁ + S₂. This is assured by the logarithmic relationship between S and P_max, as follows: If the number of microstates corresponding to the most likely distribution of the first system is P_max1 and that of the second system is P_max2, then the number of possible microstates of the most likely distribution of the combined system is simply P_max1P_max2. It is a fundamental properties of logarithms that ln(ab) = ln(a) + ln(b), so if S₁₊₂ is the entropy of the combined system, then