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.
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