High Temperature Limit: Equal Probability of Energy States Explained

In summary, the conversation discusses the relationship between temperature, energy states, and entropy. It is mentioned that in the high temperature limit, all energy states become equally probable, and this is a general property of systems in contact with a heat reservoir. The concept of temperature is described as a Lagrange multiplier that relates to the change in entropy with respect to the average total energy. It is noted that in the high temperature limit, the change in entropy per change in energy becomes smaller, which can explain the equal probability of different energy states. The concept of maximum entropy is also mentioned in relation to the equal probability of energy states.
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Suppose you have a system with different energy states and assume that it is in contact with a heat resevoir (i.e. you know the average of the total of the system). In this case, no matter the system, it seems a general property that in the high temperature limit all energy states become equally probable. Today I saw the example of an electron in a magnetic field.
I must admit I don't have a lot of intuition for what temperature actually is. I can only see from the math that it is a Lagrange multiplier which has the property that 1/T = ∂S/∂U where U is the average total energy.
Now in the high temperature limit this says the change in entropy per change in average total energy is small. But how does this explain the equal probability of different energy states, and how is the equal probability in all explain using the ideas of maximum entropy?
 
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  • #2
With a high energy, the entropy is large, but the entropy change with changing energy gets smaller. You have many states available anyway, some additional states don't change the entropy so much any more.
 

1. What is the concept of high temperature limit and equal probability of energy states?

The high temperature limit refers to the maximum temperature at which a system can exist before it undergoes a phase transition or breaks down. Equal probability of energy states means that at this temperature, all the possible energy states of a system have an equal chance of being occupied.

2. How does the high temperature limit affect the behavior of a system?

At the high temperature limit, the behavior of a system becomes more random and disordered. This is due to the equal probability of energy states, causing the system's particles to have a higher chance of occupying higher energy states and becoming more chaotic.

3. What is the relationship between temperature and the probability of energy states?

The probability of energy states increases with temperature. As the temperature increases, the energy of the system's particles also increases, allowing them to occupy higher energy states with a greater probability.

4. How does the high temperature limit relate to the concept of entropy?

The high temperature limit is directly related to the concept of entropy, which is a measure of the disorder or randomness of a system. As the temperature approaches the high temperature limit, the entropy of the system also increases, as the particles become more disordered and randomly distributed.

5. Can the high temperature limit be exceeded?

Yes, the high temperature limit can be exceeded in certain cases. For example, in systems with strong intermolecular forces, the high temperature limit may be increased due to the energy required to break these forces. Additionally, in extreme conditions such as in nuclear fusion reactions, temperatures far beyond the high temperature limit can be achieved.

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