  When a polymer solution is uniaxially stretched and held fixed at both ends,
the solution quickly separates into droplets connected by strings and takes the
beads-on-string structure. The string then becomes thinner by capillary forces.
Here we develop a theoretical framework on viscoelastic fluids based on Onsager
principle, and apply it to the dynamics of viscoelastic filaments. We show that
the beads-on-string structure is a thermodynamic quasi-equilibrium state, and
derive an equation for the coexistence condition in the pseudo-equilibrium
state. Using the condition, we solve the evolution equation analytically and
show that the string radius and the tensile stress vary exponentially as
predicted by the classical theory of Entov and Hinch [J. Non-Newtonian Fluid
Mech. 72, 31 (1997)], but the prefactor for the tensile stress is different
from their theory and agrees with the numerical solutions of Clasen et al. [J.
Fluid Mech. 556, 283 (2006)].
