What is the ruling on and expiation for a married woman thinking about another man from the past, without there being a relationship, and how can she rid herself of such thoughts?

If a woman's feelings are merely self-talk and thoughts that she tries to repel, then there is no blame upon her. However, if she finds comfort in them and her heart is at peace with them, then she is accountable, and she must repent to Allah the Almighty. It is sufficient for her to repent between herself and her Lord, and she does not need to inform her husband.