"Nonstandard" approach to the thermodynamic limit

In a Search for a Structure, Part 1: On Entropy

“…But now-a-days this "gibberish" (almost) automatically translates to the language of non-standard analysis (Abraham Robinson, 1966) [15], [18] and even easier to that of category theory (Eilenberg-MacLane-Steenrod-Cartan-Grothendieck 's, 1945-1957).…”

Nonstandard analysis and lattice statistical mechanics: a variational principle

“…In particular we will show how the problem of limiting dynamics can be handled in the nonstandard setting. In earlier papers [12] Ostebee, Gambardella and Dresden have applied nonstandard techniques to study the thermodynamic limit. Recently Helms and Loeb [4] have considered the stochastic theory of infinite particle systems from a nonstandard viewpoint.…”

“…In §8 of [13] this question is addressed for S = Zd and any equilibrium measure v. A nonstandard approach to this topic could be developed (for related work in continuous statistical mechanics see [12]) but we will not pursue it further. 5.…”