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VOLUME 84, NUMBER 5 P H Y S I C A L R E V I E W L E T T E R S 31 JANUARY 2000 Yang-Lee Theory for a Nonequilibrium Phase Transition
 

Summary: VOLUME 84, NUMBER 5 P H Y S I C A L R E V I E W L E T T E R S 31 JANUARY 2000
Yang-Lee Theory for a Nonequilibrium Phase Transition
Peter F. Arndt
Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77, 50937 Köln, Germany
(Received 20 August 1999)
To analyze phase transitions in a nonequilibrium system, we study its grand canonical partition function
as a function of complex fugacity. Real and positive roots of the partition function mark phase transitions.
This behavior, first found by Yang and Lee under general conditions for equilibrium systems, can also be
applied to nonequilibrium phase transitions. We consider a one-dimensional diffusion model with periodic
boundary conditions. Depending on the diffusion rates, we find real and positive roots and can distinguish
two regions of analyticity, which can be identified with two different phases. In a region of the parame-
ter space, both of these phases coexist. The condensation point can be computed with high accuracy.
PACS numbers: 05.20.­y, 02.50.Ey, 05.70.Fh, 05.70.Ln
The investigation of nonequilibrium systems is a grow-
ing field in statistical mechanics and currently attracts
much attention. In this context, simple models such as
driven diffusive systems play a paradigmatic role similar to
the Ising model in equilibrium statistical mechanics. These
systems establish a simple framework in which many
phenomena can be extensively studied. Moreover, driven

  

Source: Arndt, Peter - Max-Planck-Institut für molekulare Genetik
Spang, Rainer - Computational Molecular Biology Group, Max-Planck-Institut für molekulare Genetik

 

Collections: Biology and Medicine; Biotechnology; Computer Technologies and Information Sciences; Physics