Yes, many mental health issues can be mentally exhausting.
Your brain is trying to process a lot at the same time, especially when sensory items come into play. In addition what the brain is normally processing you're adding a lot of additional information.
Emotions can really be taxing. And, unlike physical activity, you don't really have a point where you know the activity will end when it's mental.
Physical or mental activities, both have the same effect on our energy levels.
This is one of the more difficult things to understand of those who it effects. They don't see you physically doing something, so how could you possibly be tired. Unfortunately I think it's one of those things you have to live to fully understand.
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Always do right. This will gratify some people and astonish the rest.