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We suggest the existence of systems in which the statistics of a particlechanges with the quantum level it occupies. The occupation numbers in thermalequilibrium depend on a continuous statistical parameter that interpolatesbetween bosonic or fermionic and ghost-like statistical distributions. We callsuch particle states ``ninions'': they are different from anyons and can existin 3+1 dimensions. We suggest that ninions can be associated with coherentangular momentum states. In the Euclidean imaginary-time formalism, theninionic statistics can be implemented via the rotwisted boundary conditions,which are associated with the rigid global rotation of the system with animaginary angular frequency. The imaginary rotation is characterized by aPT-symmetric non-Hermitian Hamiltonian and possesses a well-definedthermodynamic limit. The physics of ninions in thermal equilibrium isaccessible for numerical simulations on Euclidean lattices. We provide a no-gotheorem on the absence of analytical continuation between real and imaginaryrotations in the thermodynamic limit. The ground state of ninions sharessimilarity with the $\theta$-vacuum in QCD. The ninions can produce negativepressure and energy, similar to the Casimir effect and the cosmological darkenergy. In the thermodynamic limit, the dependence of thermal energy of freeninions on the statistical parameter is a fractal.

Fractal thermodynamics and ninionic statistics of coherent rotational states: realization via imaginary angular rotation in imaginary time formalism