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the average temperature of a small beaker of water. In principle, a thermocouple can be used to measure the water temperature to arbitrary accuracy. However, when one does the measurement, one often finds that the thermocouple reading is noisy because of eddies in the beaker. In order to get very accurate readings, therefore one has to find a way to average over all the noise. One can use a simple beaker and measure the time average. However, an alternative idea is to take a large number of beakers that are identical to the first, place all of them in identical conditions put a thermocouple in each beaker, and average over the readings of all of the thermocouples as illustrated in Figure 3-3 34 Figure 3-3: A diagram showing how the use of multiple thermocouples can be used to lower the noise in a temperature measurement In the same way, one can calculate the thermodynamic properties of a system by a time average or by creating a series of systems that are identical to the first and then averaging over all the systems. A basic concept in this calculation is that the system samples all the macroscopic states consistent with the constraints we have imposed to control the system. We perform a multitude N of independent measurements for some property X: 1N Xobs NXi (3.6) i 1PDF Image | MOLECULAR SIMULATION STUDIES IN THE SUPERCRITICAL REGION
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