Discover Entropy and the Second Law of Thermodynamics: A Playful Way of Discovering a Law of Nature

Contents......Page 10
Preface......Page 14
Probability......Page 20
Measure of Information......Page 21
END OF TEST......Page 22
List of Abbreviations......Page 24
Acknowledgement......Page 26
1.1. The Non-Atomistic Formulations of the Second Law......Page 28
1.2. The Atomistic Formulation of the Second Law......Page 33
1.3. Entropy as a Measure of Information......Page 37
Entropy......Page 40
Snack:Who’s Your Daddy?......Page 41
CHAPTER 2 All You Need to Know but Never Dared to Admit that You Already Know......Page 44
2.1. Grouping of Objects and Assigning Measures......Page 45
a. Grouping of objects......Page 51
b. An imaginary experiment with an unfair die......Page 53
The Aperitif: Playing with Dice......Page 54
The Main Course: Hierarchy of Events......Page 58
The Dessert: Children’s Perception of Probability......Page 62
Aperitif: Playing the 20-Questions Game......Page 65
The Main Course: Hierarchy of Information......Page 71
A Dart Hitting the Board......Page 82
The New Game of Marbles in Cells......Page 86
The Easiest Game You Ever Played......Page 90
The Dessert: Children Playing the 20Q Game......Page 92
Snack: Newsworthy, News Crazy......Page 96
Snack: Fifty-Percent Off or a Rip-Off?......Page 97
3.1. Initial Warm-Up: Two Marbles in Two Cells......Page 100
The Ensemble Interpretation......Page 103
The Frequency Interpretation......Page 104
3.2. Two Cells and a Varying Number of Marbles......Page 107
3.3. Ten Marbles and Varying Number of Cells......Page 118
3.4.1. A Process of Expansion......Page 123
3.4.2. Combination of Two Non-Empty Games......Page 124
3.4.3. Pure Mixing of Two Types of Marbles......Page 125
3.4.5. Mixing and Expansion......Page 127
3.4.6. Assimilation and Expansion......Page 128
Snack: How to Tell the Difference Between an Honest and a Pseudo-Honest Person (adapted from Mero (1990))......Page 130
Snack: Stray and Pay......Page 132
CHAPTER 4 Discover the Boltzmann Distribution......Page 136
4.1. Six Marbles in Three Cells......Page 138
4.2. Nine Marbles in Varying Number of Cells......Page 142
4.3. Ten Cells and Variable Number of Marbles......Page 146
4.4. Some Simple Processes Involving Transferring of Marbles......Page 149
4.4.3. Pure Assimilation......Page 150
4.5. Dependence of SMI and W on the String Length TL......Page 151
4.6. A Process Involving Exchange of String Between Two Systems......Page 155
4.7. A Spontaneous Transfer of String from the High-Value to a Lower-Value TL......Page 159
4.8. Another Experiment Involving a SpontaneousTransfer of String......Page 165
4.9. What Have We Learned in this Chapter?......Page 170
Snack: How to Choose Between Two Equal-Probability Alternatives......Page 172
Snack: The Virtuous Sheila on the FerrisWheel......Page 174
CHAPTER 5 Discover the Maxwell–Boltzmann Distribution......Page 178
5.1. Six Marbles in Three Cells......Page 180
5.2. Nine Marbles in Varying Number of Cells......Page 181
5.3. Chaning the Number of Marbles in a Fixed Number of Cells......Page 184
5.4. Dependence on the Total Cloth Area......Page 190
5.5. A Process Involving Exchange of Cloth Between Two Systems......Page 193
5.6. A Process Involving a Spontaneous Transfer of Cloth......Page 195
5.7. What Have We Learned in this Chapter?......Page 197
Snack: Klutz and Botch......Page 198
Snack: The Importance of Units......Page 199
6.1. Summary of the Experiments with a Single System......Page 200
6.1.1. The Uniform Distribution: Shannon’s First Theorem......Page 201
6.1.2. The Boltzmann Distribution: Shannon’s Second Theorem......Page 204
6.1.3. The Maxwell–Boltzmann Distribution: Shannon’s Third Theorem......Page 206
6.2. Summary and Conclusions Regarding the Processes Involving Two Systems......Page 207
The expansion process......Page 208
Mixing and expansion......Page 209
6.2.2. Evolution of a Pair of Boltzmann-Type Games......Page 210
6.2.3. Evolution of a Pair of Maxwell–Boltzmann Type Games......Page 212
6.3. Summary of Everything We Have Learned: What,Why, and How......Page 213
Snack: The Mystery of the Missing Bike and the Power of the Ten Commandments......Page 214
Snack: The Ever Reliable Cuckoo Clock......Page 217
CHAPTER 7 Entropy and the Second Law in the Real World......Page 219
7.1. The Dictionary......Page 220
7.2.1. What Happens?......Page 221
7.2.2. Why it Happens?......Page 225
7.2.3. How it Happens?......Page 228
7.3.1. An Alternative View of the Expansion Process......Page 229
7.3.2. Pure Mixing......Page 232
7.3.3. Pure Assimilation......Page 233
7.3.4. Mixing and Expansion......Page 234
7.3.5. Assimilation and Expansion......Page 236
7.3.6. A Pure De-Assimilation Process......Page 238
7.4. The Boltzmann Distribution: Shannon’s Second Theorem and Clausius’ Definition of Entropy......Page 239
7.4.1. The Boltzmann Distribution......Page 240
7.4.2. Clausius’ Definition of Entropy......Page 241
7.4.4. Spontaneous Flow of Energy from One System to Another......Page 244
7.5. The Maxwell–Boltzmann Distribution: Shannon’s Third Theorem and Clausius’ Formulation of the Second Law of  Thermodynamics......Page 246
7.5.1. Translation......Page 247
7.5.2. Summary of What We Already Know......Page 248
7.5.3. Spontaneous Heat Transfer from a Hotter to a Colder Body......Page 249
7.6. The Conclusion of All Conclusions......Page 251
Snack: Can More Incriminating Evidence be Inculpatory?......Page 255
Notes to Self-Testing Kit......Page 259
Notes to Chapter 1......Page 261
Notes to Chapter 2......Page 262
Notes to Chapter 3......Page 265
Notes to Chapter 4......Page 266
Notes for Chapter 5......Page 270
Notes for Chapter 6......Page 272
Notes for Chapter 7......Page 277
Epilogue......Page 281
Postscript......Page 283
References and Suggested Reading......Page 284
Index......Page 286