Lee-Yang Zeros and Phase Transitions in Nonequilibrium Steady States

We consider how the Lee-Yang description of phase transitions in terms of partition function zeros applies to nonequilibrium systems. Here, one does not have a partition function; instead we consider the zeros of a steady-state normalization factor in the complex plane of the transition rates. We obtain the exact distribution of zeros in the thermodynamic limit for a specific model, the boundary-driven asymmetric simple exclusion process. We show that the distributions of zeros at the first- and the second-order nonequilibrium phase transitions of this model follow the patterns known in the Lee-Yang equilibrium theory.

Figure 1

Dynamics of the ASEP. The arrow labels indicate the rates at which the corresponding transitions occur; site labels are also indicated.

Figure 2

Phase diagram of the ASEP.

Figure 3

Zeros of the normalization (3) in the complex-$\alpha$ plane for $\beta =\frac{1}{3},1$. In both cases, the lattice size $N$ is 300.

Figure 4

Zeros of the normalization (3) in the complex-$\xi =\alpha (1-\alpha )$ plane for $\beta =\frac{1}{3}$, 1 and $N=80$, 160, and 320.