Entropy Demystified

The following sections are included:

• Preface

• Contents

The following sections are included:

• The Non-Atomistic Formulation of the Second Law

• The Atomistic Formulation of the Second Law

The following sections are included:

• The Classical Definition

• The Relative Frequency Definition

• Independent Events and Conditional Probability

• Three Caveats
  • Conditional probability and subjective probability
  • Conditional probability and cause and effect
  • Conditional probability and joint probability

• A Teaspoon of Information Theory

• A Tip of a Teaspoon of Mathematics, Physics and Chemistry

• A Matter of Lottery

• A Matter of Order-Disorder

• A Challenging Problem

• Answers to the Problems
  • Answers to the roulette problems
  • Answer to “a matter of lottery”
  • Answer to “a matter of order-disorder”
  • Answer to “a challenging problem”

The following sections are included:

• One Die

• Two Dice

• Three Dice

• Four Dice and More

The following sections are included:

• Two Dice; N = 2

• Four Dice; N = 4

• Ten Dice; N = 10

• Hundred Dice; N = 100

• Thousand Dice; N = 1000

• Ten Thousand Dice; N = 10⁴ and Beyond

The following sections are included:

• See it with your Visual Sense

• Smell it with your Olfactory Sense

• Taste it with your Gustatory Sense

• Hear it with your Auditory Sense

• Feel it with your Touch (Tactile) Sense

After having experienced various manifestations of the Second Law with dice, it is time to pause, analyze and rationalize what we have learned so far. We recall that we have observed different phenomena with different mechanisms. We shall see in the next chapter that some of these examples (color, taste and scent) have counterparts in real experimental systems. Other examples cannot be performed using particles (single particles do not emit sound waves; and the temperature that we feel with the tip of our fingers is a result of the distribution of velocities. One just cannot assign a temperature to each molecule). There are of course many more examples. The central question that concerns us in this chapter is: What are the features that are common to all the phenomena that we have observed in the experiments described in Chapters 4 and 5? The phenomena discussed in this chapter are essentially the same as those in Chapters 4 and 5, except that N is very large, much larger than the largest value of N discussed previously.

The following sections are included:

• The Correspondence with the Expansion Process

• The Correspondence with the Deassimilation Process

• Summary of the Evolution of the System towards the Equilibrium State

• Mixing of Three Components

• Heat Transfer from a Hot to a Cold Gas

• Test Your Understanding of the Second Law

The following sections are included:

• What is the Source of the Mystery?

• The Association of Entropy with “Disorder”

• The Association of Entropy with Missing Information

• Is the Second Law Intimately Associated with the Arrow of Time?

• Is the Second Law of Thermodynamics a Law of Physics?

• Can We Do Away with the Second Law?

• References and Suggested Reading