The totally asymmetric simple exclusion process (TASEP) is a cornerstone of non-equilibrium statistical mechanics. Particles enter a one-dimensional chain at rate α on the left, hop rightward when the next site is empty, and exit at rate β on the right. Each site holds at most one particle. The system exhibits three phases: low-density, high-density, and maximum-current, with transitions determined by α and β relative to a critical value of 1/2.
Baryshnikov and Stolyar extend this to a multi-floor model: each site can hold up to c particles, and a particle hops forward when its site has strictly more particles than the next site. For c = 1, this reduces to standard TASEP. For c > 1, something unexpected happens.
Maximum flux — the throughput of 1/4 that represents the system's maximum carrying capacity — kicks in at a lower critical α than in standard TASEP. Specifically, for β between 1/2 and 1 with c > 1, the maximum-current phase begins earlier. Adding capacity per site makes the system saturate sooner, not later.
The intuition that more capacity should delay saturation is wrong because the back-pressure dynamics change. In standard TASEP, a particle can only move if the next site is empty — a binary condition. In the multi-floor model, a particle moves when its site has more particles than the neighbor. This creates a gradient-driven flow that is more sensitive to density differences. Small imbalances propagate faster, and the system reaches its maximum throughput before the arrival rate would saturate a standard single-floor chain.
The phase diagram changes qualitatively, not just quantitatively. New phase boundaries emerge that have no analog in c = 1. The extra capacity doesn't simply rescale the original problem — it introduces genuinely new behavior. The system with more room reaches its limits faster.