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yep! So for instance, if heat is being released from System into Surroundings, System q will be negative and Surroundings q will be positive because the surroundings are absorbing heat. Further, System T should be higher than Surroundings T. These differing values will give you a different change in entropy value for the system versus the surroundings, unless its isothermal, which in that case it will just be opposite signs.
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