Entropy as a measure of energy gradient?

[weezy]

This video explains the entropy concept as in terms of useless and useful energy. My question is how is this concluded from say Clausius' statement of 2nd law of thermodynamics which states that there can exist no cycle that transfers heat from A to B without producing any other effect. I haven't been introduced to the concept of free energy but from what I grasped if a two systems have the same energy (there could be a temperature difference) then there should be no interaction between them?

 

[Khashishi]

Your title is wrong. It's not an energy gradient. You probably got the idea from the video which shows systems with high and low temperature regions mixing to give a medium temperature region (with higher overall entropy). The video isn't wrong, but it doesn't get into the mathematical depth to understand exactly what entropy is.

You may want to check out Chet's insight: https://www.physicsforums.com/insights/grandpa-chets-entropy-recipe/

I grasped if a two systems have the same energy (there could be a temperature difference) then there should be no interaction between them?

No. Equilibrium is governed by the intrinsic variables like temperature and pressure and chemical potential, not by the energy, which is an extrinsic variable (that is, it is additive and scales with the size of the system). Note that a 100 m^3 block of ice has more energy than a 200cm^3 cup of coffee, but energy will flow from the coffee to the ice. When the temperatures are equal (in the coffee cup) there's no more flow of heat. When the pressures are equal (across the dam), there will be no more flow of fluid volume. When all intrinsic qualities are in equilibrium, then entropy is at the maximum and nothing interesting happens anymore.