What is the link between chaos and ergodicity in mechanical systems?

AI Thread Summary
Ergodic mechanical systems are defined by their time averages equaling ensemble averages and their ability to visit every point in phase space. Chaotic systems, which approach attractors and do not cover all phase space, are generally not ergodic. However, the relationship between chaos and ergodicity is complex, as some systems can exhibit both characteristics, referred to as "strongly chaotic systems." It is important to note that only dissipative systems possess attractors. Understanding these concepts is crucial for studying the dynamics of mechanical systems.
Frank Peters
Messages
28
Reaction score
2
There are many formal definitions of an ergodic mechanical system.

1) A system whose time average equals the ensemble (space) average.

2) A system that visits every point in its phase space.

Etc.

What are some actual, real examples of an ergodic mechanical system?

Also, since a chaotic system approaches an attractor and
does not visit all of its phase space, then a chaotic system
is not ergodic. Is this a correct statement?
 
Physics news on Phys.org
The link between chaos and ergodicity is more complicated. Some systems can be both chaotic and ergodic, and some authors call these "strongly chaotic systems" (see Ott, Chaos in Dynamical Systems). Note also that it is dissipative systems that have attractors.

Have a look at: http://biotheory.phys.cwru.edu/phys414/LebowitzPenrose.pdf
 

Thread '1:1 versus 2:1 Mechanical Advantage debate'

The rope is tied into the person (the load of 200 pounds) and the rope goes up from the person to a fixed pulley and back down to his hands. He hauls the rope to suspend himself in the air. What is the mechanical advantage of the system? The person will indeed only have to lift half of his body weight (roughly 100 pounds) because he now lessened the load by that same amount. This APPEARS to be a 2:1 because he can hold himself with half the force, but my question is: is that mechanical...
View full post »

Thread 'Newton's first law?'

Some physics textbook writer told me that Newton's first law applies only on bodies that feel no interactions at all. He said that if a body is on rest or moves in constant velocity, there is no external force acting on it. But I have heard another form of the law that says the net force acting on a body must be zero. This means there is interactions involved after all. So which one is correct?
View full post »
Thread 'Beam on an inclined plane'

Thread 'Beam on an inclined plane'

Hello! I have a question regarding a beam on an inclined plane. I was considering a beam resting on two supports attached to an inclined plane. I was almost sure that the lower support must be more loaded. My imagination about this problem is shown in the picture below. Here is how I wrote the condition of equilibrium forces: $$ \begin{cases} F_{g\parallel}=F_{t1}+F_{t2}, \\ F_{g\perp}=F_{r1}+F_{r2} \end{cases}. $$ On the other hand...
View full post »

Similar threads

Physicists Fix Economics: Ole Peters' Ergodic Hypothesis
Replies
1
Views
2K
I Virial Theorem and the Ergodic hypothesis
Replies
2
Views
3K
Orbital mechanics: is ballistic capture possible without acceleration?
Replies
7
Views
1K
Modeling a mechanical power system
Replies
9
Views
1K
How Does Non-Ergodicity Impact the Resting State of Living Cells?
Replies
2
Views
2K
I need sources to learn about dynamic systems
Replies
4
Views
1K
The definition of generalised momentum
Replies
43
Views
4K
Impact of chaos on a system's entropy
Replies
1
Views
6K
I Chaos vs purely exponentially growing systems
Replies
3
Views
2K
I Work-Energy Theorem for Moving Block and Spring System?
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top