  The entropic approach to dissociation of bound states immersed in strongly
coupled systems is developed. In such systems, the excitations of the bound
state are often delocalized and characterized by a large entropy, so that the
bound state is strongly entangled with the rest of the statistical system. If
this entropy $S$ increases with the separation $r$ between the constituents of
the bound state, $S = S(r)$, then the resulting entropic force $F = T\
{\partial S}/{\partial r}$ ($T$ is temperature) can drive the dissociation
process. As a specific example, we consider the case of heavy quarkonium in
strongly coupled quark-gluon plasma, where lattice QCD indicates a large amount
of entropy associated with the heavy quark pair at temperatures $0.9\ T_c \leq
T \leq 1.5\ T_c$ ($T_c$ is the deconfinement temperature); this entropy $S(r)$
grows with the inter-quark distance $r$. We argue that the entropic mechanism
results in an anomalously strong quarkonium suppression in the temperature
range near $T_c$. This "entropic self-destruction" may thus explain why the
experimentally measured quarkonium nuclear modification factor at RHIC (lower
energy density) is smaller than at LHC (higher energy density), possibly
resolving the "quarkonium suppression puzzle" - all of the previously known
mechanisms of quarkonium dissociation operate more effectively at higher energy
densities, and this contradicts the data. Moreover, we find that near $T_c$ the
entropic force leads to delocalization of the bound hadron states; we argue
that this delocalization may be the mechanism underlying deconfinement.
