Path Functions

A warning: this post starts with thermodynamics, but it will end with disruptive development. There are many compelling analogs between the two, but this post will focus on the idea of state and path functions.

From a thermodynamic perspective, a state function is a property of a system that exist at a moment in time. There are many properties like this: mass, temperature, etc.

On the other hand, there are properties known as path functions that represent the transition of the system from over a period of time. These properties include: heat transfer, work done by or on the system, etc.

Lets highlight the difference with an example: We take two cups of water both open to the atmosphere (at a pressure of 1 atmosphere). Cup A starts at 85°C and Cup B starts at 95°C. We heat each of the cups up 10 degrees so that Cup A is now at 95°C and Cup B is at 105°C. Up until this point we have only discussed the state functions associated with the system and, let’s be frank, it has been pretty boring.

However, if you are familiar with the Celsius scale you will realize that the water in Cup B at a temperature of 105°C has completely boiled away and is now steam. It turns out when we look at the heat transfer path function, we put roughly 50 times more energy into Cup B than Cup A to accomplish what appeared at first to be the same state function process. What an interesting, if not totally unforeseen, outcome.

The reason we may have been caught off-guard in the previous example is that we did not anticipate the path function of water. In thermodynamics we inherently are drawn to state functions and feel more comfortable using them. As a fairly firm rule, we try to force path functions to act like state functions whenever possible, and we (me especially) are chronically hampered when developing new thermal systems by our dependence on them.

In order to develop cutting edge thermal storage, power, and management systems, we must acknowledge and work with path functions. This is requiring many industries to developed entirely new modeling methodologies, rules of thumb, and development approaches.

Now, back to the Analogue. State and path functions are definitions used so that humans can understand the difference between things happening during a snapshot and things happening over time. The concept is not limited to thermodynamics. In fact, it is a perfect analogy for how we measure and investigate startup companies developing new technology.

Just like thermodynamics we are inherently drawn to the state functions of development because we are more comfortable with them. Market size, cash in the bank, number of patents, product ROI, and cash flow are all examples of state functions we look at when talking about startups.

And just like thermodynamics the path functions are ultimately what we care about and are what our brain is the worst at predicting: funding required to get cash positive.

Just like our two cups of water scenario, you can imagine two startups at similar late stages of development and all they need is a temperature rise of 10°C to make it. But startup B will require an unexpected 50x more in funding over startup A. 

What is most interesting is how we rely so heavily on state function advise to solve path function problems. When someone is successful, or gathers a lot of data about other people who were successful they write a book that contains a list of state functions for those companies and individuals. This is a major reason why the multitude of books about startups and disruptive technology have not made it particularly easier to run a disruptive company or put together a successful startup.

Books inherently capture one set of opinions at one snapshot, but what we really need is a guide to the infinite daily decisions and steps that make up the path function of technology development. That is more of less impossible to put into a book; especially considering that by the time the author writes the book they only remember the state functions of creating their startup anyway.

To some level the thermodynamics analogue can offer part of the solution to this problem. When people first started characterizing materials they had no idea what to expect. They could readily measure state functions, but had no idea how to predict path functions. It was only when they took materials and started experimenting with them that they figured out path functions could be predicted as they can be today. The same can be said for disruptive technology, we have a lot of state functions but don’t fully understand how they can be used to accurately predict the path. Mind you, it took us hundreds of years and massive amounts of work to figure the thermodynamic side out. So I figure, we have some time still in the lab ahead of us.

P.S. Just to show I don’t hate all, or even the majority of books about startups, the last paragraph has some serious Lean Startup Themes…