Explore the fascinating world of entropy, order, and disorder in this comprehensive lecture by renowned physicist Daan Frenkel from the University of Cambridge. Delve into the shifting perspectives on entropy as a measure of disorder since the mid-20th century, examining intriguing examples where entropy increases with increasing order. Gain insights into Gibbs' paradox and discover how recent numerical tools allow for the computation of close and distant relatives of Boltzmann's entropy. Journey through topics such as thermodynamics, hard-sphere liquids, entropic ordering in complex structures, and the relationship between entropy and granular materials. Learn about the challenges in counting distinct jammed states, the strange nature of high-dimensional basins, and the applications of these concepts in materials discovery and deep neural networks. Engage with thought-provoking discussions on Gibbs' statistical mechanics, the treatment of identical particles, and the Edwards hypothesis in granular systems.
Overview
Syllabus
DATE :29 August 2018, 16:00 to
Lecture 1: Tuesday 28 August, 16:00 to
Lecture 2: Wednesday 29 August, 16:00 to
Lecture 3: Thursday 30 August, 16:00 to
The ICTS Campus - Imagined?
ICTS and its Mandate
ICTS Research
ICTS Programs
ICTS Programs - Directions
ICTS Programs - Numbers
ICTS Programs - A Sampling
ICTS Outreach - Initiatives
ICTS Outreach-Kaapi with Kuriosity
Thank You See you again at ICTS
Introduction to Speaker
[Order, disorder and entropy Lecture - 01 by Daan Frenkel]
Outline
Thermodynamics
Rudolf Clausius
Lvdwig Boltzmann
In 1901 Planck wrote:
S = k In W
Entropy is commonly understood as a measure of disorder.
Example
The "intuitive" version of the Second Law of Thermodynamics:
2. ENTROPY: The Computer Age
Hard-sphere liquid Cannot pay energy
The 2nd Law is not violated
1986: Hard-sphere colloids really freeze
Entropic Ordering Can Lead to Complex Structures
Coordination Number Dense Fluid
KIRKWOOD's GRAVE
Entropy driven formulation of liquid crystals of rod-like colloids
3. Entropy and Sand
Relation to Mechanically Stable Disordered Packings of Slightly Soft Repulsive Particles
Sketch of the d-N dimensional energy landscape of overcompressed, soft particles.
Can we count the number of distinct jammed states numerically
How do we count the number of distinct, disordered states?
To compute the "hyper-volume" of the basin of attraction of a given jammed state we must use a free-energy' calculation:
High dimensional basins are strange
The basins are not at all like hyper-spheres
Can we associate an extensive "entropy" with the number of distinct states?
But the volumes are not all the same. Hence basins are not equally populated:
Granular entropy versus N
The same numerical tools may have applications in materials discovery and in the study of deep neural nets
Dividing by N! seems arbitrary.. but it is not
What do the textbooks say?
Van Kampen
Enter Jaynes: "Usually, Gibbs' prose style conveys his meaning in a sufficiently clear way..."
GIBBS's Sentence
Two systems of 'identical' dilute colloidal solutions in equilibrium low-fat milk
Treat as gas of N labeled but otherwise identical particles
When the two systems are in equilibrium,
Back to the Edwards hypothesis:
It appears that, precisely at unjamming, all packings are equally likely!
Taught by
International Centre for Theoretical Sciences
