  We propose to use quantum information notions to characterize thermally
induced melting of nonperturbative bound states at high temperatures. We apply
tensor networks to investigate this idea in static and dynamical settings
within the Ising quantum field theory, where bound states are confined fermion
pairs - mesons. An equilibrium signature of meson melting is identified in the
temperature dependence of the thermal-state second R\'enyi entropy, which
varies from exponential to power-law scaling. Out of equilibrium, we identify
as the relevant signature the transition from an oscillatory to a linear
growing behavior of reflected entropy after a thermal quench. These analyses
apply more broadly, which brings new ways of describing in-medium meson
phenomena in quantum many-body and high-energy physics.
