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4
votes
1answer
98 views

Caldeira-Leggett Dissipation: cannot get it

I am trying to understand the Caldeira-Leggett model. It considers the Lagrangian $$L = \frac{1}{2} (\dot{Q}^2 - (\Omega^2-\Delta \Omega^2)Q^2) - Q \sum_{i} f_iq_i + \sum_{i}\frac{1}{2} (\dot{q}^2 - ...
1
vote
1answer
143 views

Does Lyapunov exponent equate to exponential inflation?

Physics can be modeled by dynamical systems $f^t(x)$ as well as by PDEs. The most common dynamical system has hyperbolic fixed point and can be an attractor or a repellor. The dynamics at repellors ...
3
votes
0answers
43 views

Reference for the Landau-Lifshitz system

I'm interested in understanding the dynamics of the discrete Landau-Lifshitz system. It's solutions to equations like $$\frac{\partial X_n}{\partial t} = X_n\times (X_{n-1}+X_{n+1})$$ where the $X_n$ ...
3
votes
0answers
73 views

Kolgomorov entropy issues

I am long been confused by these entropy terms. Would be obliged if an explanation is provided in less technical jargon What are the differences between Shannon's entropy, topological entropy and ...
2
votes
0answers
21 views

What does unfolding of attractor mean?

What does unfolding of attractor mean? Effect of time scales on the unfolding of neural attractors paper talks about Takens embedding theorum. It says that the embedding dimension should be large ...
0
votes
0answers
31 views

Logistic map and attractors

Does the logistic map have a strange attractor for some "chaotic" values of the parameter?
0
votes
0answers
84 views

Degree-degree correlations in networks

In their paper Specificity and Stability in Topology of Protein Networks (Science 2002) Maslov and Sneppen introduced a null-model to evaluate degree-degree correlations in networks. Maslov also ...
0
votes
0answers
31 views

Is there a thermodynamic law or theorem that expresses how systems “break” or “change” when enough energy is added?

I have a simple question about thermodynamic laws, and I am hoping you can help me. Let's say that I have a sphere container with some pressurized gas in it. I can slowly increase the pressure over ...