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Time dependent function
- This ensemble average is a time dependent function, also for systems in equilibrium. It describes the average evolution of the phase function g, given that at time t0 < t the value of the phase function f was f0.
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The ensemble is defined as a set of all possible outcomes of a stochastic process, and ensemble average means the expected object (like expected value for random variable) of the stochastic process. Simply speaking it is just the expected value of random variable, but defined for a more general abstract setup.
Ensemble average. In statistical mechanics, the ensemble average is defined as the mean of a quantity that is a function of the microstate of a system, according to the distribution of the system on its micro-states in this ensemble.
Aug 29, 2023 · Ensemble averaging is a data acquisition method that enhances the signal-to-noise of an analytical signal through repetitive scanning. Ensemble averaging can be done in real time, which is extremely useful for analytical methods such as:
May 14, 2022 · 4.2: Ensemble Averages. Page ID. Franz S. Hover & Michael S. Triantafyllou. Massachusetts Institute of Technology via MIT OpenCourseWare. The other set of statistics we can compute are across the ensemble, but at a particular time. Set yi = xi(to) y i = x i ( t o) where to t o is a specific time.
22.2. Computing ensemble averages. Let’s build up how to compute an ensemble average step by step. For example let’s say we have the following data in Table 22.1. Notice how all the simulations ( sim1, sim2, sim3) share the variable t in common, so it makes sense to plot them on the same axis in Figure 22.3.
This ensemble average is time independent for systems in equilibrium. In an experiment one usually measures an unconditional ensemble average, that is, the system is not prepared in a certain state before the experiment is started.
Nov 21, 2015 · Mathematical Subject Classification. 82B03; 82-08. Short Definition. Macroscopic properties of materials can be computed from the laws of statistical physics as averages of some functions of the phase-space variables with respect to a probability measure describing the state of the system.
