Burn in question and evaluation before burn in

Generally for me they sound bright first,but some electronics I remember my Thor Audio Electronics had actually 3 different phases of burn in ...From bright to dark and then to perfect.......I would assume it could go either way..

We all experienced sound transformation before and after a new equipment or cable is burned in

Your question is excellent - I see absolutely no reason to assume that gear should be better with burn in. Why can't it get worse too? How do you know when it should finally sound good or correct?

I tend to avoid the type of gear that changes audibly. Manufacturers can design gear to be dramatically less affected by burn-in by simply designing it in such a way that it less sensitive to the things that do drift with use (capacitors, driver compliance for example).

I am wondering if there is a general rule as to which direction any burn in would be heading

Seems to me to be pretty logical that the answer would be no. Obviously it would be dependent on the type of component (amp, cd player, preamp, speaker, interconnect cable, speaker cable, etc. etc.); and on the technology used (tube, solid state, dynamic speaker, electrostatic speaker, cone driver, dome driver, ribbon driver, electrostatic membrane, etc. etc.); the specific design of the particular example of the component type and technology, etc., etc.

I agree with Shadorne's comments as well.

Regards,
-- Al