> For the complete documentation index, see [llms.txt](https://ethereum-model-of-the-world.gitbook.io/ethereum-a-model-of-the-world-1/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://ethereum-model-of-the-world.gitbook.io/ethereum-a-model-of-the-world-1/part-i/free-energy-and-entropy.md).

# Free Energy and Entropy

A **progressive** and **unrelenting** ***increase in disorder*** characterizes the nature of our world (and universe) as we understand it. Naturally, spontaneous processes exhibit an **intrinsic tendency** towards ***wasting or dissipating useful (free) energy***. By **minimizing inefficiencies** in the ***misallocation*** and ***misuse*** of Free Energy, biological systems maximize their ability to antagonize disorder and reverse entropy.

Revisiting the Hierarchy of Sciences…

![](/files/-MW0d-KwKkUE1yrYLGVm)

…at some point in time the study of Entropy began with **Randomness**, which was explored as **probability** and **chance** since those times in history.

Within thermodynamic systems, **Gibbs Free Energy** was studied in chemical reactions while **Helmholtz Free Energy** was the analogue in explosive reactions. The understanding evolved to encompass **particle statistics**, probabilities of micro and macro states, and their equilibria in **statistical thermodynamics/mechanics**...

![](/files/-MW0d-Kx_Sn6DU6j3vKm)

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Basically, the study of Entropy went from chance and randomness to phases of matter (solid, liquid, gas) to **information particles** and **statistical probabilities**.
{% endhint %}

…and eventually in the form of **Information Entropy**, following the publication of *A Mathematical Theory of Communication* by Claude Shannon in the 1940s, wherein he analyzed the statistics of ***lost information***, or **uncertainty**. This uncertainty related to outcomes came to be measured with **binary digits** – **bits**. 

![](/files/-MW0d-Ky3Xs2F7ojE3DJ)

*A fair coin will have an Information Entropy of 1 binary digit (bit) per flip, because the outcome will be either Heads = 0, or Tails = 1.*

![](/files/-MW0d-KzZX19IdyIuKS8)

*On the other hand, a fixed coin will have no Information Entropy – 0 bits per flip – because the outcome is already known, so no uncertainty exists.*

{% hint style="info" %}
 No uncertainty --> no anticipation. *Is this why the market will buy the rumor, sell the news?* 
{% endhint %}

Subsequent advances in Information Theory were combined with the field of **Probability** to spawn a range of entropy types such as conditional entropy, joint entropy, and so forth…along with **another kind of Free Energy**.