20.500.12556/RUL-161813 Makroskopske fluktuacije toka solitonov v reverzibilnem celičnem avtomatu pravilo 54 Macroscopic fluctuations of soliton current in the reversible cellular automaton Rule 54 V magistrskem delu obravnavamo makroskopske fluktuacije transporta solitonov v reverzibilnem celičnem avtomatu pravilo 54, ki predstavlja enega izmed najbolj preprostih modelov integrabilne solitonske dinamike. Za opis makroskopske dinamike kiralnih solitonov uporabimo računsko ogrodje posplošene hidrodinamike, ki ponuja kvantitativno teorijo transporta v integrabilnih sistemih z uporabo konceptov integrabilnosti, hidrodinamike in kinetične teorije. Uvedemo tipične in redke fluktuacije v mnogodelčnih sistemih ter predstavimo balistično makroskopsko fluktuacijsko teorijo, s katero analiziramo tipične fluktuacije toka solitonov v obravnavanem modelu in pokažemo, da so te fluktuacije normalne. Nato z balistično fluktuacijsko teorijo izračunamo statistiko štetja pretoka solitonov skozi izhodišče in preverimo veljavnost fluktuacijske zveze Gallavotti-Cohen. Pokažemo, da stacionarni kiralni ansambli, ki maksimizirajo entropijo sistema ne predstavljajo ravnovesnih stanj. This master’s thesis deals with macroscopic fluctuations in soliton transport within the reversible cellular automaton Rule 54, which represents one of the simplest models of integrable solitonic dynamics. We employ the theoretical framework of generalized hydrodynamics to study the large-scale dynamics of chiral solitons. This framework provides a quantitative theory of transport in integrable systems by combining concepts from integrability, hydrodynamics, and kinetic theory. We introduce typical and rare fluctuations in many-body systems and present another framework, ballistic macroscopic fluctuation theory, through which we analyze the typical fluc- tuations of soliton current in the studied model and demonstrate that these fluctuations are normal. We then use ballistic fluctuation theory to calculate the full counting statistics of soliton transfer through the origin and verify the validity of the Gallavotti-Cohen fluctuation relation. Finally, we show that stationary chiral maximum-entropy states cannot be regarded as equilibrium ones. neravnovesna statistična fizika solitoni RCA54 integrabilnost posplošena hidrodinamika transportne fluktuacije balistična makroskopska fluktuacijska teorija balistična fluktuacijska teorija fluktuacijska zveza Gallavotti-Cohen nonequilibrium statistical physics solitons RCA54 integrability generalized hydrodynamics transport fluctuations ballistic macroscopic fluctuation theory ballistic fluctuation theory Gallavotti-Cohen fluctuation relation true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2024-09-14 08:15:26 2024-09-14 08:15:30 2024-09-17 11:11:25 0000-00-00 00:00:00 2024 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 143352 207805955 13951.pdf 13951.pdf 1 EBDD062E402789AF837DD33C2BE16842 0ed8e18371f05c6ce96306cada000ef094dcf2ebf0227f0ab388147819f54358 aab4b0c3-7260-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=190797 Fakulteta za matematiko in fiziko 0 0 0