# Frequentist statistical mechanics

• DrDu
In summary, the conversation discusses the relationship between statistical mechanics and the maximum entropy principle from information theory, as explained by Jaynes. There is also mention of the possibility of an orthodox frequentistic interpretation of statistical mechanics and references are requested. Jaynes' view is that all members of an ensemble are equally probable due to ignorance, while the ergodic hypothesis states that a specific system will eventually pass through every point in its phase space. This leads to the frequentist definition of probability where every member of the ensemble is equally probable. However, Jaynes criticizes this view as the recurrence time is extremely long compared to the time it takes for a measurement to be made. The conversation concludes by mentioning that there are also critiques on the Bayesian interpretation and that
DrDu
When I learned statistical mechanics, it followed the lines of the maximum entropy principle from information theory as laid out by Jaynes which can also be seen as a Bayesian statistical theory.
I wonder whether there exist some orthodox frequentistic interpretation of statistical mechanics. Any references would be great!

Yes. So you got your ensemble. Jaynes says every member of the ensemble is equally probable due to ignorance. Another interpretation is that of those using the "ergodic hypothesis" where one postulates that a specific system will in due time (on the order of poincaré recurrence time, i.e. VERY FRIGGIN LONG) pass every point on phase phase arbitrarily close. Since every member of the ensemble corresponds with one phase space point, in the frequentist definition of probability every member of the ensemble becomes equally probable. Jaynes criticized this by saying that the recurrence time is absurdishly long and that when you make a measurement, it's on the order of seconds, not age-of-the-universe. Of course there are also many critiques on the bayesian interpretation. As far as I know, it hasn't been conclusively settled (?)

## 1. What is Frequentist statistical mechanics?

Frequentist statistical mechanics is a branch of statistical mechanics that focuses on the frequentist interpretation of probability. It involves using probability theory to analyze the behavior of large systems of particles, such as gases, liquids, and solids.

## 2. How does Frequentist statistical mechanics differ from other branches of statistical mechanics?

Frequentist statistical mechanics differs from other branches, such as Bayesian statistical mechanics, in its interpretation of probability. While Bayesian statistics views probability as a measure of belief, Frequentist statistics sees it as the long-term frequency of an event occurring.

## 3. What are some applications of Frequentist statistical mechanics?

Frequentist statistical mechanics is commonly used in the study of thermodynamics, phase transitions, and chemical reactions. It is also used in various fields of physics, chemistry, and biology to model and predict the behavior of complex systems.

## 4. What are some common methods used in Frequentist statistical mechanics?

Some common methods used in Frequentist statistical mechanics include Monte Carlo simulations, partition function calculations, and ensemble averaging. These methods allow for the prediction and analysis of macroscopic properties of a system based on the microscopic behavior of its individual particles.

## 5. What are the limitations of Frequentist statistical mechanics?

One limitation of Frequentist statistical mechanics is that it can only be applied to systems with a large number of particles, as it relies on the law of large numbers. Additionally, it does not account for uncertainty or prior knowledge, which can be important in some applications.

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