Current precision is costly: Var(J)/mean(J)^2 * sigma/2 >= 1. Explore how entropy production bounds current fluctuations in a 3-state Markov chain.
TUR (Barato-Seifert 2015, Gingrich et al 2016): for any current J in NESS, the product (Var(J)/mean(J)^2)*(sigma/2) >= 1, where sigma is entropy production rate. Tighter currents always cost more dissipation - precision has a thermodynamic price.