Fundamental assumptions of statistical mechanics

In summary, the assumption that all states are equally probable is the foundation of theories on entropy and different distributions. When asked for an explanation or reason for this assumption, it is believed that scientists at the time found that it worked and it is a fundamental concept in the subject, despite seeming odd or counterintuitive. The premise that all states of the same energy are equally probable is crucial to the study of entropy.
  • #1
Mayan Fung
131
14
The assumption states that all states (or I shall say micro-states) are equally probable. This is the foundation where we construct our theories on entropy, different kind of distributions, etc.
Is there any explanation for this assumption? Or why did the scientists that time take this assumption? I mean what made them think this is so fundamental.
 
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  • #2
Perhaps the best reason for it is they found that it works. It's kind of an odd assumption, (IMO=in my opinion), and my instincts, perhaps yours also, would tell you that some states seemingly would be more likely to occur than others. It surprised me a little when I first learned the subject, and you are correct, that the entire subject is based on the premise of all states of the same energy being equally probable.
 

Related to Fundamental assumptions of statistical mechanics

1. What are the fundamental assumptions of statistical mechanics?

The fundamental assumptions of statistical mechanics are that the particles in a system obey the laws of classical mechanics, the system is in equilibrium, and the particles are indistinguishable from one another.

2. How do the fundamental assumptions of statistical mechanics differ from those of classical mechanics?

The fundamental assumptions of statistical mechanics differ from those of classical mechanics in that statistical mechanics considers the behavior of a large number of particles in a system, rather than individual particles. It also takes into account the probabilistic nature of particles and their interactions, rather than assuming determinism.

3. Why are the fundamental assumptions of statistical mechanics important?

The fundamental assumptions of statistical mechanics allow us to make predictions about the behavior of macroscopic systems based on the properties of their individual particles. This is important in understanding and explaining the behavior of complex systems, such as gases, liquids, and solids.

4. Are there any limitations to the fundamental assumptions of statistical mechanics?

Yes, there are certain situations where the assumptions of statistical mechanics may not hold. For example, in systems with small numbers of particles or in systems that are far from equilibrium, the predictions of statistical mechanics may not accurately reflect the behavior of the system.

5. How do the fundamental assumptions of statistical mechanics relate to thermodynamics?

The fundamental assumptions of statistical mechanics are the basis for understanding the thermodynamic properties of a system. By calculating the average behavior of a large number of particles, statistical mechanics can predict macroscopic properties such as temperature, pressure, and entropy, which are key concepts in thermodynamics.

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