# Entropy and the Ideal Final Result

| On 04, Aug 2008

By Joseph Marotta

Entropy is an important concept in virtually all fields of modern science. Put simply, for any configuration of a large assembly of molecules (a macro-state), there are many ways to assemble those molecules (micro-states). Entropy can be defined a number of ways: as a number of the micro-states available to every macro-state in a system, the amount of heat energy wasted in a system and the rough amount of disorder in a system.

An analogy to an engineered system, technical or non-technical can be seen as a set of requirements for the system as a macro-state; for every set of requirements placed on a system, there are a number of ways to fulfill those requirements, within a set of constraints. In short, every specific design of a system intended to fulfill requirements can be seen as a micro-state. Design degeneracy is a type of entropy that can be defined as the number of designs available to fulfill a certain set of requirements.

## Design Degeneracy

Design degeneracy can be either a useful tool or bane to project planning, as any number of engineers will prefer a particular design for a variety of reasons. Often, design particulars preferred by one engineer are not preferred by another; no two engineers will completely agree on which design to implement for fulfilling a specific set of requirements. Many systems end up as an assembly of subcomponents from a variety of designs, as a result of compromise between a team of engineers. Sometimes this approach leads to a more robust design all around the system – increasing reliability and quality through the sum of its parts. This approach leads to compromised quality and reliability as the creative visions of different engineers conflict and are compromised.

## Ideal Final Result

The ideal final result (IFR), a technique used in systematic innovation, is intended to set forth an ideal system. Often the IFR takes the form of a system where the requirements fulfill themselves through no application of external energy or materials. The IFR leads a design team through a structured set of exercises intended to design a system as close to the ideal as possible. It is not a stretch, therefore, to think of the IFR as the design with the lowest degeneracy possible. The IFR is a functional goal, however, and not a physical one, and does not specifically give a designer a physical set of requirements to be fulfilled. While the IFR may be fulfilled through a number of different designs, the number of designs that completely fulfill requirements set forth by the IFR is the minimal design degeneracy inherent in the system.

## Design Requirements

Put another way, the probability of choosing any particular design can be thought of as a function of design requirements, physical and technical constraints, time (deadlines), potential cost of the project, designer preferences and a variety of other considerations.Based on this probability, thermodynamics can help define the average design degeneracy – or entropy. Using the IFR, in essence, reduces the probability of picking any solution that does not reduce any of the parameters associated with a particular design. In this case, the entropy is described as:

where p(xi) is the probability associated with choosing any particular design, xi. Again, the IFR does not lead to a zero-entropy or zero-degeneracy condition – it leads to minimum design degeneracy. The form of the probability function could come from decision theory or some related branch of mathematics.

Think graphically; imagine that all designs are represented in a multi-dimensional space whose axes are the various design considerations (both the design requirements and the constraints), as shown in the figure below. These axes are not necessarily perpendicular to one another, and several specific designs can be found on a design plane related to the design degeneracy.Any of these axes can be considered patterns of evolution from the Theory of Inventive Problem Solving (TRIZ), thus evolutionary design potential can be examined.

 Designs in Multi-dimensional Space

Assessing evolutionary potential of a design can be a tricky endeavor, as analyzing every component of a design for its evolutionary potential and looking at patterns of evolution in the field is time-consuming at best, and intractable at worst. An alternative, taking advantage of design degeneracy, is to objectively try to catalog the different ways of designing the same system within the same location on the design plane. These alternative designs need not incorporate all of the design constraints of the original system, but should be investigated with respect to the most important constraints. The more designs that can be envisioned, the greater the evolutionary potential will be of that particular system. This same technique can also be used for assessing the relative ideality of several systems given a particular set of requirements. The more design degeneracy that exists, the further the system is from the IFR.

A similar technique resulting from design degeneracy can be used to circumvent evolutionary limits of a particular system. If a particular design has reached its evolutionary limit, or is close to it, alternative designs can be explored on a design plane consisting of the most important evolutionary trends.

## Example: Transportation

Consider transportation methods used over a short distance. If the IFR is “I want to travel two miles without stopping faster than I can walk,” then the associated functional requirements could include average speed of travel, necessity of an external fuel source (and amount consumed), adaptability to terrain, and so forth. A close-to-ideal design can take many forms with this IFR, including a bicycle, skateboard, scooter, skis or a pair of roller skates (depending on terrain). The selection of these overarching designs exhibits the baseline design degeneracy based on the IFR (possibly indicating the need for a better-defined set of functional requirements from the IFR).

Within each of these overarching designs, several subtypes exist, all with specific places along evolutionary trends. Each of these subtypes represents a design degeneracy, which exists to fulfill limitations to the IFR based on challenges encountered during the design work. A mountain bike, for example, may be further along the “segmentation” evolutionary trend than a racing bicycle, while a racing bicycle would make further use of webs and fibers (in frame design) than a mountain bike. Which particular design of bicycle should be used will depend on the relative importance of the evolutionary trends in a particular application.

## Conclusion

Leveraging the concept ofentropy – more specifically, design degeneracy –can provide an inherent adaptability in product design by prioritizing functional design requirements. Design degeneracy can also be used when trying to assess evolutionary potential of a particular product or design. The multiplicity of design around a set of functional can be then used to circumvent evolutionary potential limits, and bring the final design much closer to ideal.