The goal of my PhD research is to understand the thermodynamics of nonequilibrium steady states in quantum systems using recently developed techniques and ideas. In the recent work arXiv:1306.3192, nonequilibrium steady state density matrix for thermal flows was found in the context of CFT on a quantum wire junction (with special, simple boundary conditions at the connection point), and the current along with all its large-time fluctuations were found exactly. In my PhD, I will develop further such techniques and look at their physical implications. Using these methods and their generalizations, I will look at (heat and charge) flows in free field models, in conformal models with conformal impurities (in the context of the general theory of conformal impurities), in the context of conformal perturbation, and in massive integrable quantum field theory models. The basic ideas to be developed are that of the nonequilibrium steady state density matrix, and that of the alternative description of large-time fluctuations using stochastic processes (like Poisson processes) of charge / energy transfer. The possible physics to be understood is that of the Fourier and related laws, and more generally of the thermodynamic properties of nonequilibrium steady states.