No company is ever entitled to work you do on your own time without using company resources, although it might get messy if said work directly competes with the company.
This is a very broad assertion about laws that may differ from state to state. It gets even more complicated when you try to answer what "on your own time" means for a salaried worker, and when you consider the broad IP agreements that many companies give to their employees.
Could you point me to where I could read more, please? This doesn't match my current understanding, and it's a topic of interest for me. Thanks!