Explain Entropy & Heat Flow: Thermodynamic Formulas & Multiplicity

[aaaa202]

In my book it says: The bigger entropy of a system, the more heat from the surroundings can enter it. Now, I don't really understand why that is completely. Can anyone explain me? - both in terms of the actual thermodynamic formulas (thermodynamic identity etc.) and in terms of multiplicity?

Maybe I have misunderstood something so here is what my book says in exact words:
"The helmholtz energy F is the total energy needed to create a system minus the energy you can get for free from an atmosphere at temperature T. This energy is given by TS, where S is the final entropy of the system. THE MORE ENTROPY A SYSTEM HAS THE MORE OF ITS ENERGY CAN ENTER AS HEAT "

 

[Chestermiller]

In my book it says: The bigger entropy of a system, the more heat from the surroundings can enter it. Now, I don't really understand why that is completely. Can anyone explain me? - both in terms of the actual thermodynamic formulas (thermodynamic identity etc.) and in terms of multiplicity?

Maybe I have misunderstood something so here is what my book says in exact words:
"The helmholtz energy F is the total energy needed to create a system minus the energy you can get for free from an atmosphere at temperature T. This energy is given by TS, where S is the final entropy of the system. THE MORE ENTROPY A SYSTEM HAS THE MORE OF ITS ENERGY CAN ENTER AS HEAT "

As a Physics Forums mentor with expertise in Thermodynamics, I have no idea what this means.