  It has long been known that there is a relation between boundary sine-Gordon
theory and thermodynamics of charge neutral two-component Coulomb plasma on a
unit circle. On the other hand, recently it was found that open string
worldsheet description of brane decay can be related to a sequence of points of
thermodynamic equilibrium of one-component plasma. Here we consider a different
decay process which is specifically described by the timelike boundary
sine-Gordon theory. We find time evolution to be mapped to a one-dimensional
curve in the space of points of thermal equilibrium of a non-neutral
two-component Coulomb plasma. We compute the free energy of the system and find
that along the curve it is monotonously decreasing, defining a thermodynamic
arrow of time.
