20.500.12556/RUL-130305 Rule 54: exactly solvable model of nonequilibrium statistical mechanics We review recent results on an exactly solvable model of nonequilibrium statistical mechanics, specifically the classical rule 54 reversible cellular automaton and some of its quantum extensions. We discuss the exact microscopic description of nonequilibrium dynamics as well as the equilibrium and nonequilibrium stationary states. This allows us to obtain a rigorous handle on the corresponding emergent hydrodynamic description, which is treated as well. Specifically, we focus on two different paradigms of rule 54 dynamics. Firstly, we consider a finite chain driven by stochastic boundaries, where we provide exact matrix product descriptions of the nonequilibrium steady state, most relevant decay modes, as well as the eigenvector of the tilted Markov chain yielding exact large deviations for a broad class of local and extensive observables. Secondly, we treat the explicit dynamics of macro-states on an infinite lattice and discuss exact closed form results for dynamical structure factor, multi-time-correlation functions and inhomogeneous quenches. Remarkably, these results prove that the model, despite its simplicity, behaves like a regular fluid with coexistence of ballistic (sound) and diffusive (heat) transport. Finally, we briefly discuss quantum interpretation of rule 54 dynamics and explicit results on dynamical spreading of local operators and operator entanglement. statistical mechanics non-equilibrium systems cellular automata thermalization statistična mehanika neravnovesni sistemi celični avtomati termalizacija true false true Angleški jezik Slovenski jezik Neznano 2021-09-13 11:36:12 2021-09-13 11:36:12 2022-09-09 04:15:48 0000-00-00 00:00:00 2021 0 0 70 str. art. no. ǂ074001 Vol. 2021 Jul. 2021 0000-00-00 PostprintKoncna Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 2022-07-16 536.9 1742-5468 10.1088/1742-5468/ac096b 76119811 RAZ_Buca_Berislav_2021.pdf RAZ_Buca_Berislav_2021.pdf 1 45F21675764973756E719A489B0B2F72 0024aff7583c5c0e2f41200de0cf51a5a4a07b133216b33a41cb328e08650ec2 3022a97d-1476-11ec-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=147382 https://iopscience.iop.org/article/10.1088/1742-5468/ac096b 0 3c09d714-1476-11ec-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=147383 Fakulteta za matematiko in fiziko 0 0 0