  In the present thesis, we study the heat flow in mesoscopic one-dimensional
transport systems. Using the analysis of full counting statistics, we calculate
the cumulant generating function of the particle and heat flows and prove its
symmetry. The symmetry produces the relations among transport coefficients of
the particle and heat flows when we expand these flows with respect to the
appropriate affinities. Moreover, we consider the generalized flows which are
superpositions of the particle and energy flows. We show that we can choose the
appropriate affinities of the generalized flows and derive the relations among
their transport coefficients when we expand the generalized flows with respect
to their affinities.
