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Ergodicity
In mathematics, the term ergodic is used to describe a dynamical system which, broadly speaking, has the same behavior averaged over time as averaged over the space of all the system's states (phase space). In physics the term is used to imply that a system satisfies the ergodic hypothesis of thermodynamics.
In statistics, the term describes a random process for which the time average of one sequence of events is the same as the ensemble average. In other words, for a Markov chain, as one increases the steps, there exists a positive probability measure at step that is independent of the probability distribution at initial step 0 (Feller, 1971, p. 271).〔Feller, W. 1971 An introduction to probability theory and its applications, vol. 2, Wiley〕
Quantitative psychologist Peter Molenaar considers the ergodicity of psychological processes to be reason for a revolution in psychology to favor intraindividual change as a course of study.〔Molenaar, P. C., & Campbell, C. G. (2009). The new person-specific paradigm in psychology. Current Directions in Psychological Science, 18(2), 112-117.〕
==Etymology==
The term "ergodic" was derived from the Greek words ''έργον'' (''ergon'': "work") and ''οδός'' (''odos'': "path" or "way"). It was chosen by Boltzmann while he was working on a problem in statistical mechanics.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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