  We analyze the proton-lead collisions at the LHC energy of 5.02TeV in the
three-stage approach, previously used to successfully describe the relativistic
A-A collisions. The approach consists of the early phase, modeled with the
Glauber model, the event-by-event viscous 3+1 dimensional (3+1 D) relativistic
hydrodynamics, and the statistical hadronization at freeze-out. We show that
features typical of collective dynamics, such as the harmonic flow and the
ridge structures in the two-particle correlations in relative azimuth and
pseudorapidity, may be naturally explained in our framework. In the
proton-nucleus system the harmonic flow is generated from an initially
event-by-event deformed system and is entirely due to these initial
fluctuations. Notably, fluctuations of strength of the initial Glauber sources
which yield the observed distribution of hadron multiplicities and, at the same
time, lead to correct values of the elliptic flow coefficients both from the
two- and four-particle cumulant method, as measured by the ATLAS collaboration.
The azimuthally asymmetric flow is not modified significantly when changing the
viscosity coefficient, the initial time for the collective expansion, or the
initial size of the fireball. The results present an estimate of the collective
component in the two-particle correlations measured experimentally. We
demonstrate that the harmonic flow coefficients can be experimentally measured
with methods based on large rapidity gaps which reduce some of the other
sources of correlations.
