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What is the Spectral Form Factor?

In many papers in Random Matrix Theory [1-3] related to quantum chaos (and, in particular, to the SYK model) they analytically continuate the partition function of the system $Z(\beta)$ into $Z(\beta +...
1
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2answers
74 views

Understanding entropy, information, and randomness

In a statistical mechanics book, it is stated that "randomness and information are essentially the same thing," which results from the fact that a random process requires high information. More ...
2
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1answer
169 views

The entropy of lottery drawing machines

Suppose we have a fair lottery drawing machine where you have a container of numbered balls that is rotated many times such that interaction of the balls with themselves and the container produces a ...
1
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0answers
99 views

One consequence of the ergodic hypothesis?

this is my first question here, and I'm trying to self-learn physics from Kip Thorne's 2017 textbook "Classical Physics". IF I understand the ergodic hypothesis correctly, it is simply the statement ...
0
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1answer
224 views

Can Chaos Theory be used to explain the Ising model in paramagnetic phase?

Is it possible? How can I explain the randomness of spins in the paramagnetic phase with chaos theory? In this case, is the randomness apparent? If yes, I think the temperature would be a reasonable ...
5
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1answer
246 views

Randomness and Thermodynamics

I am currently reading The road to reality by Roger Penrose. In chapter 27 he discusses time symmetry in dynamic evolution. He defines the Second Law of thermodynamics the following way: Heat flows ...
9
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2answers
678 views

Schrodinger's “What is life ” book quote: : The laws of physics are statistical in nature [closed]

In the book What is life? by Erwin Schrodinger, he says that the laws of physics are statistical in nature. Today, thanks to the ingenious work of biologists, mainly of geneticists, during ...
4
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3answers
2k views

Difference between “Random motion” and “Brownian motion”?

I know "Random motion" is non-deterministic unpredictable motion of a particle. But it seems "Brownian motion" has some form of determinism as we can predict the pattern created by path taken by ...
1
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0answers
434 views

Why is a random walk's RMS distance from the starting position$\propto\sqrt{N}$? [closed]

Why is the root mean squared (RMS) distance from the starting position of a (1D, 2D, or 3D) random walk of $N$ equally-sized steps proportional to $\sqrt{N}$? Is it also$\propto\sqrt{N}$ for $n$-...
4
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1answer
2k views

What exactly is entropy? Why is it measure of randomness? [duplicate]

What exactly is entropy? Why is it measure of randomness? I have been told Entropy is measure of randomness and it increases everytime randomness increases. What is Randomness? Randomness in what? ...