I'm having some trouble understanding this concept. Why is it that you sometimes can get heat for free from the environment? Like suppose you have a system, on which you make an energyconsuming proces which creates entropy. Then you subtract TΔS because apparantly heat can enter when the entropy increases - why is that? Does the temperature drop, when we increase the entropy? Can you guys please explain in terms of microstates too, as it is that way I feel I understand it the best. Also, how do you know that the temperatures between the environment and the system is the same AFTER it has absorbed exactly TΔS?