Why is there a change in entropy in a irreversible isothermic process? Suppose you have a irreversible isothermal process. The net change in entropy from the system to the surroundings should be 0 if the temperature does not change. So why is there an increase in entropy? Is it because in only an ideal situation you would be able to keep the temperature constant? Does fluctuation cause $\Delta Q/T$ to increase?
 A: We note the existence of an irreversible, isothermal thermodynamic process during which the entropy increases which is an explicit counterexample to your claim that

The net change in entropy from the system to the surroundings should be 0 if the temperature does not change.

Consider a classical ideal gas initially confined by a partition to one half of a rigid, thermally insulated container by a partition.  If one drills a hole in the partition, then the gas will freely expand to fill the entire container.  Since the container is insulated, the heat transferred to the gas is zero during this process, $Q=0$, and since the gas expanded freely, no work is done on the gas, $W=0$, so by the First Law of Thermodynamics, the change in internal energy of the gas is zero, $\Delta U = 0$.  It follows that since $U=cNk_BT $ for a classical ideal gas, and since the particle number of the gas does not change during this process: $\Delta T = 0$.  This process is also irreversible and is accompanied by a positive change in entropy $Nk_B\ln 2$.
No consideration of fluctuations is necessary.
