I'd like to ask for an example in which the minimum energy principle is used (thermodynamics). However, I've never seen a question in which examples are required, so I got the doubt that it's not allowed to ask for examples.
Questions asking for examples are list questions, discussed on meta already at e.g. Good list, bad list, May I ask a big-list question?, When are questions with multiple different possible answers good?, Question asking rare examples of the use of SO(8) and Spin(8) triality.
Overall the question you have in mind is likely to be off-topic.