Efficiency takes many forms in different disciplines. The essence of efficiency in each area is basically the ratio of the amount of stuff put into the system compared to the amount of product.
Physics
Efficiency within physics most often deals with work as in
W = F x A
With a given system (such as a engine) efficency relates to the amount of work that is able to do compared to the amount of fuel (most often heat) it is supplied.

Similarly, efficency is often used referring to power creation comparing the theoretical energy stored in a substance compared to the energy produced. The efficiency of a solar cell is the amount of energy that is produced compared to how much hits it (currently, solar cells are at about 10-15% efficiency).

Efficiency also plays a large role in the transmission of power from one place to another. In almost every case (superconductivity is the exception), it costs energy to move energy from one place to another, be it microwave beaming, the resistance inherent to power lines or mechanical friction.

Construction
With the creation of an object with a particular task in mind, the question of efficency is what can do the task with the minimal resources used?

The classic example of an efficient design within construction is the arch. Prior to the discovery of the arch by the Romans, pillars were used to hold up things (such as ceilings). Given the properties of the construction material there is a maximum distance two pillars can be to hold up a given weight. The discovery of the arch allowed builders to space the pillars further apart and thus a much more efficient structure.

Another classic example of efficency within construction is that of the suspension bridge which allows builders to build massive bridges that transverse great distances with minimal use of materials. This is an example of a tensegrity structure which uses materials that used for tension and compression in such a way that each compliments the other and show remarkable building strength that is hard to achieve with either independently.

Finally, within construction, energy efficiency is often mentioned in terms of heating, cooling and lighting. This refers to the cost of either heating, cooling or lighting an area to a particular level. The glass walled buildings that are common in California are rarely seen in the Midwest because they are very inefficient when it comes to heating in the winter or cooling in the summer because of the transmission of heat through the glass.

Economics
Within economics, there are two areas where efficiency play a role: production and labor.

With production, efficiency is the ratio of the output to the resources used. The manufacturing of integrated circuits (chips) has a theoretical maximum output of which only some percentage of the chips work correctly. Efficiency plays a role in the area of the silicon wafer that is usable and in the process used to create the chips. Chip-makers are working on both sides to make larger wafers (more area), smaller chips (less area used per item), and better yield (higher percentage of good chips).

Secondly, with labor efficiency is used in terms of workers. Given a period of time, how much work does an individual accomplish. Such things as going to the bathroom, going to get food, making telephone calls, and even noding chip away at the amount of work that an individual accomplishes. For this reason, much of management is concerned with how to make people working more efficient. Sometimes this takes the form of on site food services (people no longer have to leave the area for lunch), or groups and organizations to assist in worker happiness (a happy worker typically is more efficient than an unhappy one). Other times, this takes the form of regulations and big brother type roles to make certain that the worker does not spend time working on other tasks not related to the work at hand.

For much more than I could ever home to understand, please look at economic efficiency.

Ef*fi"cience (?), Ef*fi"cien*cy (?), n. [L. efficientia.]

1.

The quality of being efficient or producing an effect or effects; efficient power; effectual agency.

The manner of this divine efficiency being far above us. Hooker.

2. Mech.

The ratio of useful work to energy expended.

Rankine.

Efficiency of a heat engine, the ratio of the work done an engine, to the work due to the heat supplied to it.

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