These three lectures cover a certain aspect of complexity and black holes, namely the relation to the second law of thermodynamics. The first lecture describes the meaning of quantum complexity, the analogy between entropy and complexity, and the second law of complexity. Lecture two reviews the connection between the second law of complexity and the interior of black holes. Prof. L. Susskind discusses how firewalls are related to periods of non-increasing complexity which typically only occur after an exponentially long time. The final lecture is about the thermodynamics of complexity, and uncomplexity as a resource for doing computational work. The author explains the remarkable power of one clean qubit, in both computational terms and in space-time terms.
This book is intended for graduate students and researchers who want to take the first steps towards the mysteries of black holes and their complexity.
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Part I Lecture I: Hilbert Space is Huge |
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3 | (2) |
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5 | (2) |
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7 | (2) |
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9 | (2) |
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11 | (2) |
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13 | (2) |
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15 | (6) |
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7.1 Relative Complexity of Unitaries |
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17 | (2) |
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7.2 Complexity is Discontinuous |
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19 | (2) |
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8 Graph Theory Perspective |
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21 | (10) |
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24 | (7) |
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9 The Second Law of Quantum Complexity |
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31 | (8) |
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9.1 Hamiltonian Evolution |
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34 | (5) |
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Part II Lecture II: Black Holes and the Second Law of Complexity |
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39 | (2) |
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11 The Black Hole-Quantum Circuit Correspondence |
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41 | (4) |
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41 | (1) |
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11.2 Circuits and Black Holes |
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42 | (3) |
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12 The Growth of Wormholes |
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45 | (8) |
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12.1 Properties of Growth |
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49 | (1) |
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49 | (4) |
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13 Exponential Time Breakdown of GR |
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53 | (2) |
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54 | (1) |
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55 | (6) |
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55 | (3) |
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14.2 Lyapunov and Rindler |
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58 | (1) |
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14.3 Back to Size and Complexity |
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58 | (3) |
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15 Precursors and Black Holes |
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61 | (4) |
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15.1 Instability of White Holes |
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63 | (2) |
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16 Complexity and Firewalls |
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65 | (8) |
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16.1 Firewalls are Fragile |
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68 | (1) |
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16.2 What Happens After Exponential Time? |
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69 | (2) |
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16.3 The Fragility of Complexity Equilibrium |
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71 | (2) |
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17 Do Typical States Have Firewalls? |
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73 | (6) |
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73 | (1) |
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17.2 Evaporating Black Holes |
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74 | (5) |
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Part III Lecture III: The Thermodynamics of Complexity |
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79 | (2) |
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81 | (2) |
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83 | (4) |
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20.1 The Auxiliary System |
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83 | (1) |
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20.2 Combining Auxiliary Systems |
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84 | (3) |
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21 Uncomplexity as a Resource |
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87 | (2) |
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22 The Power of One Clean Qubit |
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89 | (4) |
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90 | (1) |
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22.2 Expending Uncomplexity and Negentropy |
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91 | (2) |
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23 Spacetime and Uncomplexity |
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93 | (4) |
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93 | (1) |
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23.2 Geometric Interpretation of Uncomplexity |
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94 | (3) |
| Appendix: Conclusion |
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97 | |
Leonard Susskind is an American physicist, who is professor of theoretical physics at Stanford University, and founding director of the Stanford Institute for Theoretical Physics. His research interests include string theory, quantum field theory, quantum statistical mechanics and quantum cosmology.He is a member of the US National Academy of Sciences, and the American Academy of Arts and Sciences, an associate member of the faculty of Canada's Perimeter Institute for Theoretical Physics, and a distinguished professor of the Korea Institute for Advanced Study.Susskind is widely regarded as one of the fathers of string theory. He was the first to give a precise string-theoretic interpretation of the holographic principle in 1995 and the first to introduce the idea of the string theory landscape in 2003.
Susskind was awarded the 1998 J. J. Sakurai Prize, and the 2018 Oskar Klein Medal.
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