Self-similarity, fractality and entropy principle in collisions of hadrons and nuclei at Tevatron, RHIC and LHC
$z$-Scaling of inclusive spectra as a manifestation of self-similarity and
fractality of hadron interactions is illustrated.
The scaling for negative particle production in $Au+Au$ collisions
from BES-I program at RHIC is demonstrated. The scaling variable $z$ depends
on the momentum fractions of the colliding objects carried by the
interacting constituents, and momentum fractions of the produced objects
in the scattered and recoil directions, which carries
the inclusive particle and its counterpart, respectively.
Structures of the colliding objects and fragmentation processes in final state
are expressed by fractal dimensions.
Medium produced in the collisions is described by a specific heat.
The scaling function $\psi(z)$ reveals energy, angular, multiplicity, and flavor independence.
It has a power behavior at high $z$ (high $p_T$). Based on entropy principle
and $z$-scaling, energy loss as a function of the collision energy,
centrality and transverse momentum of inclusive particle is estimated.
New conservation law including fractal dimensions is found.
Quantization of fractal dimensions is discussed.
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