Thermodynamics: Where exactly does microscopic turn to macroscopic?

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The transition from microscopic to macroscopic in thermodynamics is not defined by a specific distance scale but rather by the number of particles involved. Statistical methods can effectively describe systems with as few as 100 particles, while larger systems may still exhibit noticeable effects even with around 10^12 particles. The subtlety of the effects being analyzed influences this transition point. Understanding this relationship is crucial for applying thermodynamic principles accurately. Overall, the shift from microscopic to macroscopic behavior is complex and varies with the system's characteristics.
mikeph
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Looking for a rough distance scale over which statistical methods begin to work, and macroscopic thermodynamic variables begin to make sense. Thanks
 
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It is rather not distance scale, but number of particles involved.

It depends on how subtle effects you want to describe.
Sometimes 100 particles may be successfully treated as a thermodynamical continuum, sometimes 1012 or so still produce visible effects (Brownian moves) beyond continuous thermodynamics.
 

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