This thesis investigates the behavior of Ohmic contacts (OCs) within quantum hall edge systems, examining their significance in quantum transport phenomena across four different projects. This work includes a review of established findings on the OC, revisiting the heat Coulomb blockade in both single and multichannel configurations. The authors suggest the OC as a model within a transmission line (TL) framework to tackle dissipation potentially stemming from microscopic disorder, addressing the “missing heat� paradox and questioning prevailing theories on energy dissipation. Moreover, the authors investigate the effects of non-local couplings in drift-diffusion systems, demonstrating how they circumvent equilibrium constraints in a single edge state to facilitate heat transfer through correlations caused by interactions. The thesis examines OCs with self-looping edge states to analyze states similar to those in non-local TL systems, uncovering intriguing properties such as anomalous correlation functions and altered electrical and thermal response coefficients. Using a Langevin-like method, the authors analyze the impact of the heat Coulomb blockade on heat noise power and temperature fluctuations, showing that the temperature-temperature correlation function in equilibrium takes on a universal form and uncovering non-Gaussian Full Counting Statistics in transmitted charge as a result of temperature fluctuations. Lastly, this thesis sets the groundwork for future studies, offering a collection of ideas and projects for further exploration, aiming to contribute as a valuable resource for ongoing and future research in quantum transport phenomena. In a broader context, this thesis significantly enhances our comprehension of correlations and heat transport within interacting low-dimensional systems, paving the way for advancements in electronics miniaturization, precision metrology, and the realization of quantum information technologies.