Integrable multi-phase thermodynamic systems and Tsallis' composition rule

Abstract

We derive a class of equations of state for a multi-phase thermodynamic system associated with a finite set of order parameters that satisfy an integrable system of hydrodynamic type. As particular examples, we discuss one-phase systems such as the van der Waals gas and the effective molecular field model. The case of N −phase systems is also discussed in detail in connection with entropies depending on the order parameter according to Tsallis' composition rule.

On quantum and relativistic mechanical analogues in mean-field spin models

“…Such an analogy has been pointed out and investigated over the past few decades, and tracing back in time the genesis of such an approach, because of the vast popularity of these magnetic mean-field models, is not a simple task. Newman pointed out the analogy in 1981, as did Bogolyubov and co-workers in the early 1980s [1,2]; more recently, Choquard & Wagner [3] as well as the present authors and colleagues (see [4][5][6][7][8] and also [9][10][11][12]) have done the same.…”

“…Such an analogy has been pointed out and investigated over a few decades and tracing back in time the genesis of such an approach, due to the vast popularity of these magnetic mean field models, might be not a simple task. Brankov and Zagrebnov in 1983 used the analogy to accurately describe the Husimi-Temperley model in [8] 1 and also Newman already pointed out this analogy early in the eighties and even more recently Choquart and Wagner in 2004 [9] and the present authors and colleagues (see [16,2,14,4,3] and also [19,10,12] and [21]). However, the discovery of such an analogy turns out to be nothing but the tip of an iceberg demanding a further exploration.…”