# Between classical or quantum statistics

• GotTrips
In summary, the difference between quantum statistics and classical statistics lies in the application of microscopical dynamics and the 6 postulates of nonrelativistic quantum mechanics. The Gibbs' paradox highlights the need for quantum statistical physics, which accounts for the paradox by considering the dimensionless volume element on the phase space.

#### GotTrips

Hi can someone please help me! Can someone explain when it is acceptable to quantum statistics instead of classical statistics? And what is the difference between them.

Thanks All

OLY

I don't remember the eqn but the critical word is "thermal wave length" that describes the difference between two. Look at th Huang's Statistical Mechenics for details

Microscopical dynamics and the application of the 6 postulates of (nonrelativistic) QM is the decisive factor...

Think of the Gibbs' paradox and u'll understand the need for a quantum statistical physics...

Daniel.

dextercioby said:
Microscopical dynamics and the application of the 6 postulates of (nonrelativistic) QM is the decisive factor...

Think of the Gibbs' paradox and u'll understand the need for a quantum statistical physics...

Daniel.

Seratend.

The Gibbs paradox is accounted for quite nicely even in classical statistic if one considers the dimensionless volume element on the phase space

$$d^{2s}\tilde{x}=:\frac{1}{h^{2s}}\prod_{i=1}^{2s} dq_{i}dp_{i}$$

to which the VI-th postulate is applied to

$$d^{2x}x^{*}=:\frac{1}{h^{2s}N!}\prod_{i=1}^{2s} dq_{i}dp_{i}$$

Daniel.

Last edited:

## 1. What is the difference between classical and quantum statistics?

Classical statistics is based on classical physics principles and is used to analyze data from macroscopic systems. It assumes that all particles in a system can be observed and measured simultaneously. Quantum statistics, on the other hand, is based on quantum mechanics principles and is used to analyze data from microscopic systems. It takes into account the probabilistic nature of subatomic particles and their interactions.

## 2. Can classical statistics be applied to quantum systems?

No, classical statistics cannot be applied to quantum systems because it does not take into account the probabilistic nature of subatomic particles. It also does not consider the effects of quantum phenomena such as superposition and entanglement.

## 3. What are the main applications of classical statistics?

Classical statistics is commonly used in fields such as economics, biology, and social sciences to analyze data from large-scale systems. It is also used in engineering and quality control to ensure the reliability and efficiency of processes and products.

## 4. What are the main applications of quantum statistics?

Quantum statistics is primarily used in physics and chemistry to analyze data from subatomic and atomic systems. It is also applied in fields such as materials science, nanotechnology, and quantum computing.

## 5. Which type of statistics is more accurate?

The accuracy of statistics depends on the system being analyzed. Classical statistics is more accurate for macroscopic systems, while quantum statistics is more accurate for microscopic systems. Both types of statistics have their own limitations and are used in different contexts depending on the nature of the data being analyzed.