I understand that there is an arc flash boundary when someone if performing energized work on equipment. But, what about equipment such as a high voltage 13.8KV distribution panel in a room and no one is working on it. Is there a boundary or can someone without PPE work next to the panel such as sweeping the floor, mopping the floor, etc.

You can mop the floor. Boundaries are present when there are "exposed live parts". If an electrician has the door open, the boundaries are in effect and the electrician should have the area barricaded off out to the arc flash protection boundary, so no "unqualified" employees will be able to cross in to the danger zone. Electrical equipment should be maintained to reduce the hazard of arc flash around electrical equipment. Doors should be shut and all latches should be engaged. Electrical equipment should be engineered to direct an arc flash through the roof. If they are not, then new equipment may be warranted. Hope this helps.

Read the definition of arc flash. You have to be interacting with the equipment in a way that can trigger an arc flash. It has nothing to do with whether the doors are open or not. Same with exposed conductors. Some (a lot) of well maintained equipment has nothing exposed even with open doors. Do not mix up arc flash and shock hazards. They are two entirely different hazards.

Triggering an arc flash does not seem to be neccessarily caused by "interacting with the equipment." There is a body of events out there that shows "Arc-in-a-Box" occurances have occasionally occurred without interaction by qualified maintenance personnel. It means the painted floor lines for exclusion zones are important for all without PPE to obey including janitors, managers, tourists, etc. Not arguing with you, just promoting extreme caution. Another EE forum has extensive discussion about this issue. I recall as a young engineer being 30 feet away from an enclosed breaker which decided to explode when it tried to open. Scared the you-know-what out of me. Tom Parkhill, PE.

70E does not preclude the possibility of spontaneous arc initiation, and this is in the definition. However it is well recognized that the likelihood is low if it can be assumed that equipment is properly maintained, which is also not only required through multiple passages in Article 200 but reinforced in the hazard analysis sections of Article 130. IEEE standard 493 gives estimated event rates for these spontaneous arcing faults down around 10^-6 per year for most cases, or 1 in a million. Existing standards for tolerable risk rates consider this acceptable.