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The same numerical tools may have applications in materials discovery and in the study of deep neural nets
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Order, Disorder and Entropy - Lecture 1
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- 1 DATE :29 August 2018, 16:00 to
- 2 Lecture 1: Tuesday 28 August, 16:00 to
- 3 Lecture 2: Wednesday 29 August, 16:00 to
- 4 Lecture 3: Thursday 30 August, 16:00 to
- 5 The ICTS Campus - Imagined?
- 6 ICTS and its Mandate
- 7 ICTS Research
- 8 ICTS Programs
- 9 ICTS Programs - Directions
- 10 ICTS Programs - Numbers
- 11 ICTS Programs - A Sampling
- 12 ICTS Outreach - Initiatives
- 13 ICTS Outreach-Kaapi with Kuriosity
- 14 Thank You See you again at ICTS
- 15 Introduction to Speaker
- 16 [Order, disorder and entropy Lecture - 01 by Daan Frenkel]
- 17 Outline
- 18 Thermodynamics
- 19 Rudolf Clausius
- 20 Lvdwig Boltzmann
- 21 In 1901 Planck wrote:
- 22 S = k In W
- 23 Entropy is commonly understood as a measure of disorder.
- 24 Example
- 25 The "intuitive" version of the Second Law of Thermodynamics:
- 26 2. ENTROPY: The Computer Age
- 27 Hard-sphere liquid Cannot pay energy
- 28 The 2nd Law is not violated
- 29 1986: Hard-sphere colloids really freeze
- 30 Entropic Ordering Can Lead to Complex Structures
- 31 Coordination Number Dense Fluid
- 32 KIRKWOOD's GRAVE
- 33 Entropy driven formulation of liquid crystals of rod-like colloids
- 34 3. Entropy and Sand
- 35 Relation to Mechanically Stable Disordered Packings of Slightly Soft Repulsive Particles
- 36 Sketch of the d-N dimensional energy landscape of overcompressed, soft particles.
- 37 Can we count the number of distinct jammed states numerically
- 38 How do we count the number of distinct, disordered states?
- 39 To compute the "hyper-volume" of the basin of attraction of a given jammed state we must use a free-energy' calculation:
- 40 High dimensional basins are strange
- 41 The basins are not at all like hyper-spheres
- 42 Can we associate an extensive "entropy" with the number of distinct states?
- 43 But the volumes are not all the same. Hence basins are not equally populated:
- 44 Granular entropy versus N
- 45 The same numerical tools may have applications in materials discovery and in the study of deep neural nets
- 46 Dividing by N! seems arbitrary.. but it is not
- 47 What do the textbooks say?
- 48 Van Kampen
- 49 Enter Jaynes: "Usually, Gibbs' prose style conveys his meaning in a sufficiently clear way..."
- 50 GIBBS's Sentence
- 51 Two systems of 'identical' dilute colloidal solutions in equilibrium low-fat milk
- 52 Treat as gas of N labeled but otherwise identical particles
- 53 When the two systems are in equilibrium,
- 54 Back to the Edwards hypothesis:
- 55 It appears that, precisely at unjamming, all packings are equally likely!
