A system is isolated when there is no energy exchange with the surroundings. For example the contents of a vacuum flask are isolated. In practice there is an error in the isolation parameter, i.e. delta(energy) that is why after some time the contents will be found to be in room temperature. Experiments are designed so as to work within the errors.
The universe is by definition of the word isolated, because it contains everything by definition, and thus there can be no exchange of energy with anything. If there could be, it would be counted within the universe.
Now models may be found where "universe" is defined with some error in this energy exchange. Even speculated as many isolated ones, but there would be no way of knowing since no energy would be exchanged.
It has to do with the definition of entropy.
P_i is the probability that the system is in the ith microstate, and k_b is the Boltzmann constant.
The number of microstates increase in time when there are energy exchanges.
For the isolated universe the microstates increase in time because we have experimental evidence that the universe is expanding. As the volume gets larger the number of possible microstates increases