In my career, I've witness & experienced the negative side-effects of working in highly competitive and intellectual environments, usually results in what we call "burning out" but I prefer to call "mental fatigue".
I'm not a psychologist but here's my telltale signs that you are about to burn out or experience deep mental fatigue.
Self destructive decision making.
If you find yourself taking impulsive self-destructive career decisions, that is a good indication that your subconscious reactive mind is trying to get you out of a bad situation, at it's most basic level, sometimes by just getting you fired.
You can only reach calmness by sleeping.
This means your mind is gasping for air, if you don't have any moments of emotional neutrality during the day, something is wrong and you probably switching into a reactive mode.
Constant sense of fear.
Something I witness a lot in the start-up world, from entrepreneurs & also investors. It's an indication you are losing perspective, letting the business or the market control you. An economy base on fear of "missing the next big thing" is destined to crash as well for anyone associated with it.
Deep underlying anger.
Anger comes from lost of control, it's a reactive state and good indication something very subtle is bothering you at a sub-conscious level. Usually it's something that you are trying to avoid facing on a conscious layer.
Your problems feel bigger than you.
Probably the clearest indication that you are burning out, it usually it means you are not able to manage the complexity of your professional situation. If the current negative context persist, your cognitive reasoning abilities will probably shut down and you will be in a reactive mode, you will not be able to take optimal decisions and will have only your instincts to survive, your only hope then, is that they good.
You must be aware that the human mind runs on energy like your body and muscles. If you abuse it, it will tear itself apart. The emotional cognitive space seeks a certain degree of comfort & security, even you are not constantly conscious of it and it will self-destruct if it's unable to process any solutions. Over a certain level of stress, sleep or death becomes equals to the mind.
So it's only by being truly & deeply aware of yourself and your context, you will be able to prevent mental fatigue.