Second law of thermodynamics

The second law of thermodynamics specifies the characteristic change in the entropy of a system undergoing a real process. The law accounts for the irreversibility of natural processes, and the asymmetry between future and past. For a system without exchange of matter with the surroundings, the change in system entropy exceeds the heat exchanged with the surroundings, divided by the temperature of the surroundings. In the idealized limiting case of a reversible process, the two quantities are equal, and the total entropy of system and surroundings remains unchanged. When heat exchange with the surroundings is prevented, the law states that in every real process the sum of the entropies of all participating bodies is increased.
The second law is an empirical finding that has been accepted as an axiom of thermodynamic theory. Statistical thermodynamics, classical or quantum, explains the microscopic origin of the law.

The second law states that there exists a useful state variable called entropy S. The change in entropy delta S is equal to the heat transfer delta Q divided by the temperature T.

ΔS = ΔQ / T

the combined entropy of the system and the environment remains a constant if the process can be reversed. If we denote the initial and final states of the system by "i" and "f":

Sf = Si (reversible process)