Something I don't understand about work, heat, and entropy.

[zeromodz]

I've been doing a lot of research on how the sum of a systems change and the environments change from point a to be always increases in entropy for irreversible processes. My question really has to do with heat and work during maximum entropy.

Once a system reaches maximum entropy where the temperature is completely uniform. I understand that no heat can be extracted from the system, but why does that necessarily mean there will be no more work? I know that there are other ways that can perform work like gravity, atomic forces, electric potential, and so forth. Heat transfer isn't the only way to extract work right? Why do all these sources I read from say that after a system reaches maximum thermodynamic entropy, no more work is performed?

 

[Mapes]

Maximum entropy implies that a system exhibits not only uniform temperature, but also uniform pressure, electrical charge, magnetic field, stress, surface tension, and so on.

 

[atyy]

It refers to macroscopic work. The Carnot cycle efficiency depends on a temperature gradient. If this is violated, then there should be trouble for the second law of thermodynamics, since the Carnot cycle run backwards is used to prove the equivalence of the Kelvin and Clausius statements.