Transient behavior of full counting statistics in thermal transport

The generating function of energy counting statistics is derived for phononic junction systems. It is expressed in terms of the contour-ordered self-energy of the lead with shifted arguments, $\Sigma^A(\tau, \tau') = \Sigma_L\bigl(\tau +\hbar x(\tau), \tau' + \hbar x(\tau')\bigr) - \Sigma_L(\tau, \tau')$, where $\Sigma_L(\tau,\tau')$ is the usual contour-ordered self-energy of the left lead. The cumulants of the energy transferred in a given time $t_M$ from the lead to the center is obtained by taking derivatives. A transient result of the first four cumulants of a graphene junction is presented. It is found that measurements cause the energy to flow into the lead.