This post explains entropy, primarily defining it as a measure of uncertainty. It introduces:

1. Shannon Entropy (Information Theory): Quantifies uncertainty as the expected 'surprise' or minimum bits needed to describe a system's state, dependent on outcome probabilities.
2. Physical Entropy (Statistical Mechanics): Relates entropy to the logarithm of the number of microscopic states (microstates) corresponding to a macroscopic observation (macrostate). Higher entropy means more possible microstates for a given macrostate.
3. Entropy and Time: The apparent 'arrow of time' (why systems tend towards mixing/equilibrium) arises because systems evolve towards macrostates with vastly more corresponding microstates (higher entropy), assuming the universe started in a low-entropy state (Past Hypothesis). Microscopic laws are time-reversible, but macroscopic behavior appears irreversible due to statistics and coarse-graining.
4. Clarifications: Addresses apparent violations (e.g., refrigerators, life) by noting entropy must increase for the total system. Critiques the analogy of entropy as mere 'disorder'.

#Entropy #StatisticalMechanics #InformationTheory #ArrowOfTime