Theory of nonequilibrium first-order phase transitions for stochastic dynamics

Journal of Mathematical Physics

Volumn 39, Issue 3, 1998, Pages 1517-1533

  Gaveau, Bernard ^a   Schulman, L S ^b  

^a SORBONNE UNIVERSITÉ   (France)

^b CLARKSON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032332306     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532394     Document Type: Article

References (26)

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21. The "fundamental intuition" of phase coexistence has been incorporated in other definitions of phase transition, some of them stemming from the C* algebra approach (Refs. 25 and 26). In this language a phase transition is expressed by the nonuniqueness of the infinite volume Gibbs measure. As indicated, we do not know how to bring infinite volume (the thermodynamic limit) into so mild a form of nonequilibrium as metastability, nor do we think that such a limit best reflects the physics (cf. Ref. 6).
22. 1") must be small in some sense for our phases to be well-defined, but the measure of smallness in that equation can probably be replaced by something weaker.
23. 1 need not be writable as a sum of one-dimensional projections and a Jordan form would be required. See the remark following Eq. (3.4).
24. M is small.
25. D. Ruelle, Statistical Mechanics: Rigorous Results (Benjamin, New York, 1969).
26. D. Ruelle, "The C*-algebra approach to statistical mechanics," in Statistical Mechanics at the Turn of the Decade, edited by E. G. D. Cohen (Marcel Dekker, New York, 1971), p. 67-79.