Entropy and a Book of Orders In thermodynamics, Heat, Temperature, Pressure, Work and Entropy are the...
In thermodynamics, Heat, Temperature, Pressure, Work and Entropy are the main ensemble of variables that describe how mechanical/cyclical engines operate. The second law of thermodynamics was a big deal when it was discovered. The models of the cycle of these engines sparked the industrial revolution. Example the Carnot Heat Engine. Chemistry and chemical engineering fields also enjoyed a boon of discoveries and applications and products. All these are bound and constrained by this notion of Entropy.
Around the same time, late 1800s, Willard Gibbs ‘discovered’ the same Entropy in statistical models of the world. This statistical Entropy worked the same way as physical entropy. Later in the 1950s Claude Shannon ‘discovered’ Entropy at Bell Labs as it relates to communications (conveying information). This entropy also obeyed the second law. Again it was a boon to understanding and building communication systems of all kinds.
I think that in the business world probabilistic models can be applied to model cyclic processes like click advertising and lead generation (supply and demand problems). Gibbs Entropy, I believe, can be used to understand the limits, constraints and optimizations of the process. I believe that these business cycles will indeed obey the second laws of thermodynamics. The ensemble of Variables in advertising: Profit, Profit Margin and Entropy are analogous to Work, Temperature and Entropy in engines. Humans seem to understand entropy well. We are constantly weighing options while we all seek our own utility. Acting to get more energy than we expend. We watch around us as once ordered things decay, rust, stop working, crumble. Famously, Claude Shannon at AT&T made the the connection between Entropy, bandwidth and information content.
I have abducted his Theorem (actually others are calling it Gibbs-Shannon Entropy) and eagerly explore this same entropy as an oracle for decision making for optimal consumption, in this case, an optimum ad serving strategy.
I think we can calculate the value of a Book of CPC advertisers using Entropy. The Book is the full collection of all your CPC client Orders. “Book” for short. Temperature of the Book T is the difference between Sales (RPV) and Cost (CPC). Total Book value = Sum of (Entropy x T)
This concept applies to certain difficult marketing businesses.
In these businesses the Book of Orders (Book for short) is a company asset. It fairly can be put on the company’s Balance Sheet as the predicted sum of profit from the full depletion of the Book. It presents the ability to generate revenue in the future. The marketer’s goal is to deplete this Asset and produce the most profit for the company from this asset.
I propose that the value of this asset is proportional to the Entropy associated with the Book of Orders. The value of the Book is product of the associated Entropy H(X) and the expected gross profit of a sale (Sales T_{X} – Cost of Sales W_{X} – Cost of Goods T_{Y}).
Value = ∑_{z} H(X) ( ΔT – W_{X}) analogous to Total Energy = Σ H(x) Δ T
And here are some framework notations for a Book of Orders:
Let us define the common parameters of Orders and of supply.
Entropy associated with Order x = H(x) = n ∑_{x∈Y} – p( Y|x ) log_{b} p( Y|x ). Note that if an order falls outside of Y (x∉Y), the Entropy associated with x is zero and the order will have no value. Maximum entropy occurs when p(Y|x) = 1/2. Using log base 2 gives units of bits for the entropy. However, Jing Chen, in his paper “The Entropy Theory of Value” says that b is the number of producers of Y. hmm.
Equity is Energy. Relative Temperature is ΔT = T_{X} – T_{Y} or the difference in sales and cost (gross profit). The Balance sheet Equity E that is generated by an new Order is
E = ∑_{z} H(x_{i}) ( T_{xi} – T_{Y}(z) – W_{X}) or E = ∑_{z} H Δ T or Equity = Entropy x Change in Temperature
Likewise Equity is produced if Entropy increases while Temperature is held steady. E = T Δ H
The per Unit value of a drawn lead or page-view is V(Y|x) = – log_{2} p( Y|x ) is the log likelihood of a match and is = the number of true/false questions needed, on average, to guess if a match for order x has occurred.
Entropy of two Orders x_{1} and x_{2 } = H(X) = H(x_{1} ,x_{2} )
In general, H(x_{1} ,x_{2} ) ≤ H(x_{1} ) + H(x_{2} ). This means the book entropy can be less than the sum of entropy for each order. Equality occurs when x1 and x2 are independent. When two Orders overlap they have mutual information I.
H(x_{1} ,x_{2} ) = H(x_{1} ) + H(x_{2} ) – I(x_{1} ;x_{2} ) where I(x_{1} ;x_{2} ) is the Mutual Information of the two orders.
By Chain Rule, the Entropy of three Orders = H(X) = H(x_{1} ,x_{2} ,x_{3}) = H(x_{1} ) + H(x_{2} | x_{1}) + H(x_{3} | x_{2} , x_{1})
The chain rule offes an algorithmic approach to calculating the Entropy of a Book. The series has k calculations. Book Entropy of k Orders = H(x_{1},x_{1},x_{1},…, x_{k})
Total Value of a Book of Orders = ∑_{x} H(X(x)) (ΔT(x))
People are hungry in Edmond, Oklahoma. It is our hope to provide a source of nutritious fresh food by serving local food banks.
The garden sits in the bottom of Chisholm Creek and shows great promise with great top soil and a nice flat 1/2 acre for cultivation.
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People are hungry in Edmond, Oklahoma. There were times as a child that I was hungry. People don't get enough fresh vegetables. It is my hope to provide a source of nutritious fresh food to my community of local food banks, kitchens, friends and family.
The garden sits in the bottom land of Chisholm Creek and has great top soil and a nice flat 1/2 acre for cultivation. We have added a water well, irrigation and electricity.
The setting is my favorite reason to garden here. The old elm tree shades a nice sitting area from which to view the garden and the rich nature that comes and goes in the bottom.
For a long time now, I have been interested in modeling...
MediaAlpha is for sale. Quinstreet should buy them....
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Even in prosperous Edmond, food banks do a steady business serving the poor. Most efforts are operated by volunteers. They almost always need help. Please give cash or volunteer.
Great examples:
Regional Food Bank: where you can donate or volunteer.
Other Options, Inc. in OKC
Project66 Community Food Pantry in Edmond