Thermodynamics finds application in many areas of physics, many of them sharing the feature of fluid-like or many-body like behavior.
However, small systems or few body systems have been studied too using thermodynamics. But generally it is accepted that these systems behave differently from macroscopic systems: they are non-extensive.
Non-extensivity generally is deduced from the fact that extensive properties in these systems don't add up the way they would in macroscopic ones. But I am struggling to find hard evidence of this, because merging two systems, at least in a thermodynamics view, implies that we should check the equilibrium cases only.
I mean, when I say that for two non extensive systems with entropies $S_a$ and $S_b$ it doesn't hold $S_a + S_b = S_{a+b}$, I should be checking that all these systems are under the same conditions regarding intensive properties, right? If not, then not even macroscopic systems would exhibit extensivity.
My question is: Are there publications checking this aspects for certain small systems?
I am searching for a papers where this is checked, because I have not seen this done and find it strange.
Answer
A recent work that uses nanothermodynamics and includes a computational investigation of the kind you are asking about for an Ising lattice:
R.V. Chamberlin, The Big World of Nanothermodynamics
Sec.5 of the following paper makes a reference to another paper that appears to have tested the limits of usual thermodynamics in single polymer stretching experiments:
You may also find some clues in discussion and refs from Secs. 2.3-2.5 of this paper:
It is actually the Intro to this volume: Dynamics and Thermodynamics of Systems with Long Range Interactions, Eds. T. Dauxois, S. Ruffo, E. Arimondo, M. Wilkens (Google Books)
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