All Questions
Tagged with complex-systems statistical-mechanics
12 questions
20
votes
5
answers
10k
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What are some of the best books on complex systems and emergence?
I'm rather interested in getting my feet wet at the interface of complex systems and emergence. Can anybody give me references to some good books on these topics? I'm looking for very introductory ...
7
votes
2
answers
1k
views
Statistical Mechanics & Dynamical Systems
As a (theoretical) physics student I've taken (advanced) undergrad courses in both statistical mechanics and dynamical systems (which was purely mathematical, treatment of nonlinear differential ...
7
votes
1
answer
624
views
necessary and sufficient conditions for an isolated dynamical system which can approach thermal equilibrium automatically
Given an isolated $N$-particle system with only two body interaction, that is
$$H=\sum_{i=1}^N\frac{\mathbf{p}_i^2}{2m}+\sum_{i<j}V(\mathbf{r}_i-\mathbf{r}_j)$$
In the thermodynamic limit, that ...
- 6,071
37
votes
3
answers
5k
views
Why can't many models be solved exactly?
I have been told that few models in statistical mechanics can be solved exactly. In general, is this because the solutions are too difficult to obtain, or is our mathematics not sufficiently advanced ...
- 503
15
votes
2
answers
4k
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Which areas in physics overlap with those of social network theory for the analysis of the graphs?
I am studying social networks in terms of graph theory and linear algebra. I know that physicists have published and worked a lot in this field. This causes me to assume that there are sub-fields in ...
- 782
9
votes
1
answer
926
views
Scale invariance and self organized criticality
On wikipedia I have found this statement:
In physics, self-organized criticality (SOC) is a property of (classes of) dynamical systems which have a critical point as an attractor. Their macroscopic ...
- 836
4
votes
3
answers
941
views
What is the definition of "Complexity" in physics? Is it quantifiable?
I don't know much about the discipline of "Complex systems studies" but I know in the field of "Statistical mechanics" there is much talk about the "Complexity of the system&...
- 872
4
votes
1
answer
345
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How to compute entropy of networks? (Boltzmann microstates and Shannon entropy) [closed]
I also asked in SO here a few days ago, thought it may be also interesting for physics-related answers.
I would like to model a network as a system.
A particular topology (configuration of edges ...
- 143
7
votes
4
answers
1k
views
Physical distinction between mixing and ergodicity
How can one in a very contrasting manner distinguish between the physical meaning of mixing dynamics and that of ergodic dynamics? More precisely, is one a stronger condition than the other? (which ...
- 4,800
3
votes
2
answers
934
views
Is there a relation between complexity of a system and entropy?
Disclamer: I'm not a physics professional, so pardon me if the question is stupid/incomperhensible/generally doesn't make sense. And I've googled it, but didn't find an answer.
Getting to the point, ...
- 131
2
votes
0
answers
465
views
Liouville theorem and the ergodic assumption
I am following a course on statistical mechanics. My instructor presented us the following Liouville theorem in two (claimed) equivalent ways:
Differential statement: The probability distribution $\...
2
votes
1
answer
688
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 ...
- 389