The real problem with entropy is its affects in closed systems. Basically, they eventually they run down. To make anything exempt from or immune to entropy is not of itself, respectively, not possible.
However, if the object is permanently part of or connected to an open system whereby energy is constantly or continually flowing through or into the system, then that object won't run down. OK it will need to undergo continuous replacement and refurbishment of any bits that wear out.
Think of your entropy-exempt object as something continues to regenerate as it operates, taking in as much matter and energy as it loses. Open systems like this aren't "magically" exempt or immune to entropy, but they are more than capable of overcoming entropy's depredations.
Like JDlugosz such a system will appear to be alive. In his answer he suggested a nanosystem, this answer goes a bit further and suggests any system capable of self-repair, self-regeneration and which functions as an open system in terms of matter and energy qualifies. It may resemble an organic machine, but entropy won't take it down.
This answer has been accomplished with minimal hand-waving, and it hasn't even broken the Second Law of Thermodynamics.