What concept expands upon relationship between entropy and energy conversion? I am very confused about the following:
I would consider a perfect screw to have low entropy. Its surface is near frictionless because the arrangement of molecules is just perfectly ordered and constructed.
This screw can be used to convert one type of energy into another without losing a lot to heat energy. The lower entropy causes energy conversions to be more perfect, from one form to other form instead of creating a lot of new energy forms.
However, it took a great amount of  energy to create this perfect screw. The same can be said about a perfect sail, a perfect gear wheel..
One would almost say there is something being conserved with the energy needed to create order in the disordered universe, and the highly efficient energy conversion machines created from these objects.
Does this relationship have a name? And is it even a true statement, that a lot of energy is needed to create these low entropy objects? 
Sometimes I hear creating low entropy things is easy: just lower the temperature. But I don’t see how that’s possible without taking energy from somewhere else to tame all the random brownian motions into something that is statistically behaving in a certain way with a minimum of variation.
And, is there a relationship between minimal entropy and maximum conversion of energy forms? 
 A: Usually because that is what the second law of thermodynamics states. Entropy must always increase. Since things that create low entropy violate this law this means that it took a lot of energy to make these low entropy objects. Of course entropy can drop as long as the entropy of the universe keeps on increasing. Well I am not too sure but minimal entropy means you can not really convert energy from one form to another. There has to be a change of entropy. It is not to just have low entropy. That low entropy must then start increasing to high entropy for conversion of energy forms to occur. That is because if everywhere entropy is low then that low entropy will be the new high entropy and somewhere there will be a lower entropy. 
A: My sense is that energy and entropy are a constant shell game of sorts. Energy expenditure entails entropy increase.
I think a good tool for understanding the second law is the arrow of time.  Which you may already be familiar with.  A glass falls to shatter on the floor.  The shards of glass and any contents change from a compressed ordered form to a dispersed form. On a molecular level with the shattering of molecular bonds there is heat loss.
This process demonstrates the arrow of time as a one way street in relation to the increase if entropy because,  while a glass may fall to shatter on the floor it will not realistically,  spontaneously reform up on the table from which it fell. The shattering of the glass demonstrates the arrow,  or direction,  of time. It moves only forward as the event is an irreversible process.  You can clean up th mess and replace the glass. Or you can glue the pieces if the glass back together or you might be able to melt and recycle the shattered glass but the fall and break are not reversed to whatever extent the effects are reversed through more energy expenditure and entropy.
The same is true when calories are burned to sustain you, or gasoline is burned in a car. Both you and the car are open systems. You can replace your burned calories with food and you can put ore fuel into the gas tank of a car. The burned fuel starts out as concentrated energy potential and upon conversion, allowing the car to function,  some of the fuel is dispersed as vapors. Again an irreversible process demonstrating the arrow of time.
Getting back to the shattered water glass, where did the glass come from in the first place? Fuel is burned to melt sand, converting it into glass.  Energy expenditure,  time's arrow,  and entropy.
Entropy is disorder but it's not necessarily by the usual definition of that term. It's heat loss and the lowering of potential energy.  No one and nothing could actually function without it.
You and I, earth,  and all life are famously star stuff. Which is to say that we exist because stars aged and died, consuming themselves and losing their formidable heat potential. That is stellar scale entropy, heat loss, and an irreversible process.  But I would rather live on earth than the surface of the sun.
The arrow of time can be applied to many processes and can give a strong intuitive sense if the actual prevalence and results of entropy.  It is everywhere,  constantly.
