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The thermodynamics of rigidly rotating systems experience divergences whenthe system dimensions transverse to the rotation axis exceed the critical sizeimposed by the causality constraint. The rotation with imaginary angularfrequency, suitable for numerical lattice simulations in Euclideanimaginary-time formalism, experiences fractalization of thermodynamics in thethermodynamic limit, when the system's pressure becomes a fractal function ofthe rotation frequency. Our work connects two phenomena by studying howthermodynamics fractalizes as the system size grows. We examine ananalytically-accessible system of rotating massless scalar matter on aone-dimensional ring and the numerically treatable case of rotation in thecylindrical geometry and show how the ninionic deformation of statisticsemerges in these systems. We discuss a no-go theorem on analytical continuationbetween real- and imaginary-rotating theories. Finally, we compute the momentof inertia and shape deformation coefficients caused by the rotation of therelativistic bosonic gas.

Rigidly-rotating scalar fields: between real divergence and imaginary fractalization