Phase diagram structures in a periodic one-dimensional exclusion process

Pinned or moving: States of a single shock in a ring

Totally asymmetric exclusion processes (TASEPs) with open boundaries are known to exhibit moving shocks or delocalized domain walls (DDWs) for sufficiently small equal injection and extraction rates. In contrast, TASEPs in a ring with a single inhomogeneity display pinned shocks or localized domain walls (LDWs) under equivalent conditions [see, e.g., H. Hinsch and E. Frey, Phys. Rev. Lett. 97, 095701 (2006)PRLTAO0031-900710.1103/PhysRevLett.97.095701]. By studying periodic exclusion processes composed of a driven (TASEP) and a diffusive segment, we discuss gradual fluctuation-induced depinning of the LDW, leading to its delocalization and formation of a DDW-like domain wall, similar to the DDWs in open TASEPs in some limiting cases under long-time averaging. This smooth crossover is controlled essentially by the fluctuations in the diffusive segment. Our studies provide an explicit route to control the quantitative extent of domain-wall fluctuations in driven periodic inhomogeneous systems, and should be relevant in any quasi-one-dimensional transport processes where the availability of carriers is the rate-limiting constraint.

Quantum Fokker-Planck-Kramers equation and entropy production

We use a canonical quantization procedure to set up a quantum Fokker-Planck-Kramers equation that accounts for quantum dissipation in a thermal environment. The dissipation term is chosen to ensure that the thermodynamic equilibrium is described by the Gibbs state. An expression for the quantum entropy production that properly describes quantum systems in a nonequilibrium stationary state is also provided. The time-dependent solution is given for a quantum harmonic oscillator in contact with a heat bath. We also obtain the stationary solution for a system of two coupled harmonic oscillators in contact with reservoirs at distinct temperatures, from which we obtain the entropy production and the quantum thermal conductance.

Asymmetric exclusion process with global hopping

We study a one-dimensional totally asymmetric simple exclusion process with one special site from which particles fly to any empty site (not just to the neighboring site). The system attains a nontrivial stationary state with a density profile varying over the spatial extent of the system. The density profile undergoes a nonequilibrium phase transition when the average density passes through the critical value 1-[4(1-ln2)](-1)=0.185277..., viz., in addition to the discontinuity in the vicinity of the special site, a shock wave is formed in the bulk of the system when the density exceeds the critical density.