  We consider thermal conduction across a general nonlinear phononic junction.
Based on two-time observation protocol and the field theoretical/algebraic
method, the cumulants of the heat transferred in both transient and
steady-state regimes are studied on an equal footing, and practical formulae
for the calculation of the cumulant generating function of heat transfer are
obtained. As an application, the developed general formalism is used to study
anharmonic effects on fluctuation of steady-state heat transfer across a
single-site junction with a quartic nonlinear on-site pinning potential. An
explicit nonlinear modification to cumulant generating function exact up to the
first order is given, in which Gallavotti-Cohen fluctuation symmetry is
verified. Numerically a self-consistent procedure is introduced, which works
well for strong nonlinearity.
