Meaning of formula from statistical physics

In summary, the formula S = -k\sum_r{p_r\ln p_r} from statistical physics explains that for each state of macroscopic equilibrium, there are a large number of possible microscopic states or molecular configurations. The entropy, S, is related to the total number of possible microscopic states, p, by the Boltzmann relation. From a microscopic perspective, an increase in entropy corresponds to an increase in molecular randomness or uncertainty. This formula can also be represented as S = k*ln(p) and reduces to the textbook version if all p's are identical.
  • #1
broegger
257
0
Hi.

Can anyone explain the meaning of this formula from statistical physics to me:

[tex]S = -k\sum_r{p_r\ln p_r}[/tex]​

Ok, I know that S is the entropy, the p's are probabilities of some sort - but somehow this is not satisfactory :-)
 
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  • #2
What this formula tells you is that for each state of macroscopic equilibrium there corresponds a large number of possible microscopic states or molecular configurations. The entropy, s, of a system is related to the total number of possible microscopic states of that system, called the thermodynamic probability p, by the Boltzmann relation:

[tex] S= k*ln(p) [/tex]

So from a microscopic point of view, the entropy of a system increases when the molecular randomness or uncertainty increases.

(stole most of that from my textbook but, eh, gets the job done :tongue:)
Edit: Your formula is slightly different from mine. It appears that yours takes on the form of a probability mass function, where the sum over all r should equal to one.
 
Last edited:
  • #4
Ok, thanks guys!
 

1. What is the meaning of a formula in statistical physics?

The meaning of a formula in statistical physics is to describe the behavior of a system of particles or macroscopic objects in terms of statistical laws and probabilities. These formulas are derived from fundamental physical principles, such as conservation of energy and momentum, and can be used to make predictions about the behavior of a system.

2. How are formulas used in statistical physics?

Formulas in statistical physics are used to describe the behavior of a system by calculating the average properties of a large number of particles. This allows us to understand the behavior of complex systems, such as gases, liquids, and solids, and make predictions about their macroscopic properties.

3. What are some common formulas used in statistical physics?

Some common formulas used in statistical physics include the Maxwell-Boltzmann distribution, which describes the distribution of speeds of particles in a gas, and the Boltzmann distribution, which relates the energy of a system to its temperature. Other important formulas include the partition function, which describes the relative probabilities of different energy states in a system, and the ideal gas law, which relates the pressure, volume, and temperature of a gas.

4. How do formulas in statistical physics relate to thermodynamics?

Formulas in statistical physics are closely related to thermodynamics, as they both describe the behavior of physical systems. Thermodynamics focuses on macroscopic properties, such as temperature and pressure, while statistical physics uses formulas to describe the behavior of individual particles and how they contribute to the macroscopic properties of a system.

5. Can formulas in statistical physics be used to make predictions?

Yes, formulas in statistical physics can be used to make predictions about the behavior of a system. By inputting the appropriate variables into the formulas, we can calculate the expected values of certain properties, such as energy or temperature, and use this information to make predictions about the behavior of a system. However, these predictions are based on statistical probabilities and may not always perfectly match real-world observations.

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