Equilibrium state - statistical intuition

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SUMMARY

The discussion focuses on the concept of equilibrium states in statistical mechanics, emphasizing that all accessible microstates of a system are equally likely when in equilibrium. It highlights the necessity of equal distribution for applying entropy effectively, particularly in random and homogeneous systems such as gases. The conversation underscores that without a defined equal probability for microstates, traditional entropy calculations become invalid.

PREREQUISITES
  • Understanding of statistical mechanics principles
  • Familiarity with the concept of microstates and macrostates
  • Basic knowledge of entropy and its applications
  • Foundational grasp of probability theory
NEXT STEPS
  • Research the role of microstates in statistical mechanics
  • Explore the implications of entropy in non-homogeneous systems
  • Study the relationship between probability distributions and thermodynamic properties
  • Investigate examples of gases and their equilibrium states in detail
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Students and professionals in physics, particularly those studying thermodynamics and statistical mechanics, as well as anyone interested in the foundational principles of entropy and probability theory.

paweld
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Can anyone give me some intuitive arguments about why
all the accessible microstates of the system are equally likely in equillibrium
state.
 
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I guess there isn't an argument. If in probability theory you don't know the distribution (like the probability of a price behind one of three doors), then you assume equal distribution.

In all cases where microstates are not equally distributed you simply cannot apply entropy that way.

So in a way entropy is restricted to completely random and homogeneous systems like gases unless you find a way to define microstates with equal probabilities.
 

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