Can I put into Acknowledgments someone who is no longer living? I am finishing a paper which was created thanks to my inspiration of Erik Erikson's work on psychological developement. The paper is, however, in the field of thermodynamics and complexity-science. I, therefore, feel grateful that such a great theory was created many years ago, and now is capable to push exact sciences step forward. I named two terms following Erikson's theory. I would like to note this somewhere, or state in general that I was inspired by the theory.

Do you think that it is OK to do this? Maybe I should hold back for some time, I can always state the "thank you" in the subsequent papers?
I would reserve the acknowledgments section for people or organizations that directly contributed to the paper.  For example, if you talked with Erikson while he was still alive and he offered advice or suggestions, then it would be appropriate to thank him in the acknowledgments.  If you were just inspired by his papers, then it is better to discuss that elsewhere in the paper.  For example, you could note in the introduction that your approach is inspired by Erikson's work on psychological development, or you could mention this background when you define the terms based on his theory.  But if you thank him in the acknowledgments section, then people will assume there was a more personal connection unless you clearly specify otherwise ("Although I was never lucky enough to discuss this work with him in person, I owe Erik Erikson a great debt for...").

The main thing you should not do when thanking a deceased person is to attribute opinions to them, because they are not around to contradict you.  For example, you should not thank them in a way that suggests they supported your work, even if it's true, unless you have some documented proof.  For example, it's awkward to write "I am deeply grateful to Erik Erikson for his steadfast belief in my theory."