Entropy: a powerful property observed in Thermodynamics, Information Theory and Machine Learning
“The entropy of a message is a measure of its information content, analogous to the entropy of a thermodynamic system.” — Claude Shannon.
Entropy is a concept that appears in various fields of science and engineering. It is a measure of the amount of disorder or randomness present in a system.
In this essay, we will compare and contrast entropy as it appears in thermodynamics, information theory, and machine learning. We will describe the equations that define entropy in each of these contexts, as well as the applications of these concepts.
Thermodynamic Entropy
Thermodynamic entropy, also known as Clausius entropy, is a fundamental concept in thermodynamics. It is a measure of the amount of energy in a system that is unavailable for doing useful work. In other words, it measures the degree of disorder or randomness in a system.
The second law of thermodynamics states that the total entropy of a closed system always increases over time. This means that the amount of energy that is available for doing useful work decreases over time, and eventually the system will reach a state of maximum entropy, also known as thermal equilibrium.
