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isolated systems always go towards thermodynamic equilibrium, and that is a state with maximum entropy. An example is if you have an ice cube in a room, and the room is an isolated system, the total entropy inside the room will increase as the ice melts. The system is exchanging heat within itself and increasing entropy. Heat doensn't flow from a cooler body to a hotter body.
The entropy of an isolated system must remain constant or increase because of the number of possible states/configurations it has can only increase or remain the same, never decrease. This is because the system cannot lose energy or matter, so no molecules or energy are being lost; thus, no possible states/configurations are lost. This means that an isolated system cannot LOSE entropy.
One way of thinking of entropy is simply a measure of energy that becomes unusable. If we know that there is a fixed amount of usable energy in any given system, then it follows that there is also a fixed amount of entropy in a given system as well. If there is a fixed amount it must at some point reach a maximum. It is at that point that the entropy will not change.
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