We review the trade-offs between speed, fluctuations, and thermodynamic cost involved with biological processes in nonequilibrium states discuss how optimal these are light of universal bound set by uncertainty relation (TUR). The values product Q TUR, which can be used as a measure precision enzymatic realized for given cost, suboptimal when substrate concentration is at Michaelis constant, so...

We introduce jump processes in R, called density-profile process, to model biological signaling networks. They describe the macroscopic evolution of finite-size spin-flip models with k types of spins interacting through a non-reversible Glauber dynamics. We focus on the the kdimensional empirical-magnetization vector in the thermodynamic limit, and prove that, within arbitrary finite time-inter...