In this work, we discuss recent developments in the computer simulations of molecular fluids under thermal gradients. Non-equilibrium simulations allow performing numerical tests of fundamental questions of non-equilibrium thermodynamics. These tests show that non-equilibrium simulations provide an efficient approach to quantify within a single simulation the thermophysical properties of fluids along an isobar. We discuss aspects connected to the computation of local temperatures in systems under the influence of heat fluxes, and how the combination of non-equilibrium molecular dynamics and non-equilibrium thermodynamics allows understanding phenomena arising from the coupling of internal molecular variables and heat fluxes, which lead, e.g. to thermo-molecular orientation. The behavior of these orientational effects near a fluid critical point is also discussed.
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Two configurational temperature expressions are investigated from the point of view of their utility as a diagnostic tool for Monte Carlo (MC) simulations. The MC calculations were performed for systems of spherically symmetric particles in the bulk and in a channel. Different density and system size conditions are considered. It is shown that the configurational temperature based on the ratio of two averages of the force functions can serve as a suitable method for calculating the temperature for the MC simulation. This configurational temperature can signal the presence of random number correlations and can serve as a cross-check formula in MC studies of strongly confined systems.
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