Statistical Ensembles, May 24, 2024

In physics, specifically statistical mechanics, an ensemble (also statistical ensemble) is an idealization consisting of a large number of virtual copies (sometimes infinitely many) of a system, considered all at once, each of which represents a possible state that the real system might be in. In other words, a statistical ensemble is a set of systems of particles used in statistical mechanics to describe a single system.[1] The concept of an ensemble was introduced by J. Willard Gibbs in 1902.

[1] Oxford Dictionary of Physics. pp. 458

The ensemble formalises the notion that an experimenter repeating an experiment again and again under the same macroscopic conditions, but unable to control the microscopic details, may expect to observe a range of different outcomes.

The notional size of ensembles in thermodynamics, statistical mechanics and quantum statistical mechanics can be very large, including every possible microscopic state the system could be in, consistent with its observed macroscopic properties. For many important physical cases, it is possible to calculate averages directly over the whole of the thermodynamic ensemble, to obtain explicit formulas for many of the thermodynamic quantities of interest, often in terms of the appropriate partition function.

Me: OK, “including every possible microscopic state the system could be in” covers everything physical from the cosmos to biology. It boggles my mind that educated people declare “probability and statistics do not have anything to do with truth.” What about the truth of physical systems? which includes everything science deals with?

If you are talking about a God who affected the state of the universe (i.e., miracles) then you are talking about ensembles of physical states that comprise the universe having changed.

Scientists think in terms of statistics and probability. They think a physical event is believable based on it’s probability. So probability and statistics directly affect believability.

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