Fundamental assumptions of statistical mechanics

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SUMMARY

The fundamental assumption of statistical mechanics posits that all micro-states are equally probable, forming the basis for theories on entropy and various distributions. This assumption, while seemingly counterintuitive, has proven effective in explaining thermodynamic behavior. Historical scientists adopted this principle due to its empirical success in predicting outcomes in physical systems, despite initial skepticism regarding the uniform likelihood of states. The premise that states of the same energy are equally probable is central to understanding statistical mechanics.

PREREQUISITES
  • Understanding of micro-states and macro-states in thermodynamics
  • Familiarity with the concept of entropy in statistical mechanics
  • Basic knowledge of probability theory and distributions
  • Awareness of historical developments in physics related to statistical mechanics
NEXT STEPS
  • Research the implications of the equiprobability of micro-states on entropy calculations
  • Explore different types of statistical distributions in thermodynamics
  • Study the historical context and reasoning behind the adoption of the equal probability assumption
  • Learn about the role of statistical mechanics in modern physics applications
USEFUL FOR

Physicists, students of thermodynamics, and anyone interested in the foundational principles of statistical mechanics and their applications in understanding physical systems.

Mayan Fung
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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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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.
 

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