Uphill in reaction-diffusion multi-species interacting particles systems

Abstract

We study reaction-diffusion processes with multi-species of particles and hard-core interaction. We add boundary driving to the system by means of external reservoirs which inject and remove particles, thus creating stationary currents. We consider the condition that the time evolution of the average occupation evolves as the discretized version of a system of coupled diffusive equations with linear reactions. In particular, we identify a specific one-parameter family of such linear reaction-diffusion systems where the hydrodynamic limit behaviour can be obtained by means of a dual process. We show that partial uphill diffusion is possible for the discrete particle systems on the lattice, whereas it is lost in the hydrodynamic limit.

arXiv comment26 pages, 3 figures

References in corpus (19)

• Spontaneous Breaking of Translational Invariance in One-Dimensional Stationary States on a Ring
• Reaction-Diffusion Processes of Hard-Core Particles
• Quasichemical Models of Multicomponent Nonlinear Diffusion
• Stochastic $R$ matrix for $U_q(A_n^{(1)})$
• Spectrum in multi-species asymmetric simple exclusion process on a ring
• Driven tracer with absolute negative mobility
• Microscopic models for uphill diffusion
• Self-Duality for the Two-Component Asymmetric Simple Exclusion Process
• An algebraic construction of duality functions for the stochastic U_q(A_n^{(1)}) vertex model and its degenerations
• Latent heat and the Fourier law
• Non-equilibrium 2D Ising model with stationary uphill diffusion
• A Multi-species ASEP(q,j) and q-TAZRP with Stochastic Duality
• Particle models with self sustained current
• Exact solution to integrable open multi-species SSEP and macroscopic fluctuation theory
• Fourier law, phase transitions and the stationary Stefan problem
• Switching interacting particle systems: scaling limits, uphill diffusion and boundary layer
• Quantum algebra symmetry of the ASEP with second-class particles
• Ergodic theory of multi-layer interacting particle systems
• Emergence of stationary uphill currents in 2D Ising models: the role of reservoirs and boundary conditions

Cited by in corpus (1)

• Mobility-induced kinetic effects in multicomponent mixtures