B Proper Understanding of Dynamical Systems and State Space

[Gi-So-Jeong]

TL;DR Summary

I would appreciate it if you could review whether I have properly understood dynamical systems and state space in The Theoretical Minimum: Classical Mechanics by Leonard Susskind.

Proper Understanding of Dynamical Systems and State Space​

Content from The Theoretical Minimum: Classical Mechanics by Leonard Susskind (Korean Edition):
A system is defined as a collection of entities, whether they are particles, fields, waves, or anything else.

My Interpretation:
In a dynamical system, particles, fields, and waves are components that define the state of the system. The state of a system is described by a set of variables (state variables) that contain the physical information of these components. In a dynamical system, particles, fields, and waves form a system that includes physically interacting elements, which is analyzed by setting specific boundaries. The way the state of a system is described varies, but it is defined by a minimal set of variables. These variables represent the current state of the system and are essential for predicting its future motion.

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Content from The Theoretical Minimum: Classical Mechanics by Leonard Susskind (Korean Edition):
A system that is isolated from the entire universe or any other external influence and behaves as if nothing else exists is defined as a closed system.

My Interpretation:
The matter within the system of the entire universe is isolated from external material interactions, making it a closed system. However, since the thermodynamic process of energy transfer occurs as energy is emitted from the universe, it may seem as if nothing else exists, yet energy exchange still takes place. Therefore, it can be defined as a closed system.

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I would appreciate it if you could review whether I have properly understood these concepts.
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[PeroK]

Unfortunately, English is the standard language here.

 

[Gi-So-Jeong]

Unfortunately, English is the standard language here.

Thank you for letting me know. I accidentally wrote in Korean while translating into English. I appreciate your small kindness.

 

[PeroK]

Thank you for letting me know. I accidentally wrote in Korean while translating into English. I appreciate your small kindness.

In terms of classical mechanics, the entire universe is not very relevant. We are always dealing with a subset of the universe. A closed system can be anything from two particles interacting - perhaps gravitationally or electromagnetically - to the solar system. And everything in between.

Classical mechanics can't model the entire universe very well - for that you need general relativity.

 

[Ibix]

The matter within the system of the entire universe is isolated from external material interactions, making it a closed system. However, since the thermodynamic process of energy transfer occurs as energy is emitted from the universe, it may seem as if nothing else exists, yet energy exchange still takes place. Therefore, it can be defined as a closed system.

I'd say you're reading too much into this. An ideal closed system exchanges nothing with its outside environment. In reality there is always some interaction with the outside world, but it's often negligible - so we treat the system as closed.

An example of a system that isn't closed is throwing a ball to a friend, considering only you, the ball and your friend. Initially there's zero momentum, then there's some momentum while the ball is in the air, then there's no momentum again when your friend has stopped the ball. That's an open system because an external force that you didn't account for stopped you and your friend from moving when you interacted with the ball.

If you add the Earth into the system, the system is closed. You, your friend, and the Earth recoil slightly when you throw the ball, and you, your friend and the Earth recoil slightly in the opposite direction when your friend catches the ball. There are no interactions with anything else - all forces come from one part of the system pushing on another.

Now, that last is not quite true. As you say, we're exchanging heat with space and the Sun, there are gravitational interactions we didn't model - dozens of things, probably. But they're all tiny enough that they have no measurable (that's the key word!) effect, so we can treat the system as closed.

 

[A.T.]

In reality there is always some interaction with the outside world, but it's often negligible - so we treat the system as closed.

Also, often we are only interested in certain types of interactions, like momentum transfer along a specific axis, along which we want to assume Momentum conservation. Here we don't care how much momentum along the other axes is exchanged with the outside world.