Difference between statistical and dynamical properties

In summary, the main differences between statistical and dynamics properties in physics are that dynamics is described by the amplitude and is additive, while statistics is described by relative frequency and is connected to dynamics through Born's rule. The dynamics determines the statistics, but the reverse is not true because the dynamics of multiple additive terms is lost. To better understand these differences, specific examples of properties in each category are needed.
  • #1
junt
18
1
Hi All,

What are the main differences between statistical and dynamics properties in physics? Could you please explain the difference for problems in both classical and quantum mechanics. For instance, path integral molecular dynamics is supposed to give statistical properties of a quantum mechanical system. Can I say, time-dependent Schrodinger's equation gives the dynamical properties of a quantum mechanical system? What other examples of approaches can you give me to look for statistical and dynamical properties of a physical system?

Thanks!
 
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  • #2
I look at it this way:

The dynamics is described by (is additive in) the amplitude, the statistics by the relative frequency. Born's rule says they are connected since the latter is the square modulus of the former. So the dynamics determines the statistics but the reverse is not true.
 
  • #3
mikeyork said:
I look at it this way:

The dynamics is described by (is additive in) the amplitude, the statistics by the relative frequency. Born's rule says they are connected since the latter is the square modulus of the former. So the dynamics determines the statistics but the reverse is not true.
Why is the reverse not true?
 
  • #4
Because the dynamics of multiple additive terms is lost.
 
  • #5
junt said:
What are the main differences between statistical and dynamics properties in physics?

This question is way too general. Can you give some specific examples of properties in each category?
 

1. What is the difference between statistical and dynamical properties?

Statistical properties refer to the average behavior or characteristics of a system over a large number of observations, while dynamical properties refer to the behavior or characteristics of a system at a specific moment in time.

2. How do statistical and dynamical properties relate to each other?

Statistical properties are often derived from dynamical properties by analyzing the behavior of a system over time. On the other hand, dynamical properties can be used to make predictions about the future statistical behavior of a system.

3. Can you give an example of statistical and dynamical properties?

An example of a statistical property would be the average speed of a car on a highway, while a dynamical property would be the instantaneous speed of the car at a specific moment in time.

4. Which type of properties is more useful in studying complex systems?

Both statistical and dynamical properties are important in studying complex systems. Statistical properties can provide an overall understanding of the system, while dynamical properties can help to identify patterns and make predictions.

5. How are statistical and dynamical properties used in scientific research?

Scientists use statistical properties to analyze large amounts of data and draw conclusions about a system. Dynamical properties are often used to create mathematical models and simulations to better understand and predict the behavior of a system.

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