ergodicadj.

/əːˈɡɒdɪk/

Etymology: < German ergoden (L. Boltzmann 1887, in Jrnl. f. d. reine u. angewandte Math. C. 208), < Greek ἔργον work + ὁδός way + -ic suffix.

Mathematics.

Of a trajectory in a confined portion of space: having the property that in the limit all points of the space will be included in the trajectory with equal frequency. Of a stochastic process: having the property that the probability of any state can be estimated from a single sufficiently extensive realization, independently of initial conditions; statistically stationary. Also, of or pertaining to this property.

ΚΠ

1928 tr. E. Schrödinger's Coll. Papers Wave Mech. 143 The ‘ergodic hypothesis’ (Boltzmann) is what Maxwell called the ‘principle of continuity of path’.

1931 G. D. Birkhoff in Proc. National Acad. Sci. U.S.A. 17 651 I propose..to establish a general recurrence theorem and thence the ‘ergodic theorem’.

1947 R. Courant & H. E. Robbins What is Math.? (ed. 4) vii. 354 A rectangular box..leads in general to an ergodic path; the ideal billiard ball going on for ever will reach the vicinity of every point, except for certain singular initial positions and directions.

1962 E. Parzen Stochastic Processes iii. 74 In general, a stochastic process is said to be ergodic if it has the property that sample (or time) averages formed from an observed record of the process may be used as an approximation to the corresponding ensemble (or population) averages.

1967 E. U. Condon & H. Odishaw Handbk. Physics (ed. 2) v. ii. 19 The justification for the use of this ensemble would be a consequence of an ergodic theorem; that is, a theorem which states that almost all systems in the ensemble spend the same amount of time in any regions of the same (nonvanishing) area on the constant energy surface.

Derivatives

ergoˈdicity n. the quality or property of being ergodic.

ΚΠ

1949 W. Feller First Berkeley Symp. Math. Statistics & Probability 418 What ergodicity might possibly mean in practice may be illustrated by the much discussed Pareto law of income distribution.

1960 G. Herdan Type-token Math. xx. 296 Under certain circumstances a system will tend in probability to a limiting form which is independent of the initial position from which it started. This is the Ergodicity Property.

This entry has not yet been fully updated (first published 1972; most recently modified version published online June 2018).

单词	ergodic
释义	ergodicadj. /əːˈɡɒdɪk/ Etymology: < German ergoden (L. Boltzmann 1887, in Jrnl. f. d. reine u. angewandte Math. C. 208), < Greek ἔργον work + ὁδός way + -ic suffix. Mathematics. Of a trajectory in a confined portion of space: having the property that in the limit all points of the space will be included in the trajectory with equal frequency. Of a stochastic process: having the property that the probability of any state can be estimated from a single sufficiently extensive realization, independently of initial conditions; statistically stationary. Also, of or pertaining to this property. ΚΠ 1928 tr. E. Schrödinger's Coll. Papers Wave Mech. 143 The ‘ergodic hypothesis’ (Boltzmann) is what Maxwell called the ‘principle of continuity of path’. 1931 G. D. Birkhoff in Proc. National Acad. Sci. U.S.A. 17 651 I propose..to establish a general recurrence theorem and thence the ‘ergodic theorem’. 1947 R. Courant & H. E. Robbins What is Math.? (ed. 4) vii. 354 A rectangular box..leads in general to an ergodic path; the ideal billiard ball going on for ever will reach the vicinity of every point, except for certain singular initial positions and directions. 1962 E. Parzen Stochastic Processes iii. 74 In general, a stochastic process is said to be ergodic if it has the property that sample (or time) averages formed from an observed record of the process may be used as an approximation to the corresponding ensemble (or population) averages. 1967 E. U. Condon & H. Odishaw Handbk. Physics (ed. 2) v. ii. 19 The justification for the use of this ensemble would be a consequence of an ergodic theorem; that is, a theorem which states that almost all systems in the ensemble spend the same amount of time in any regions of the same (nonvanishing) area on the constant energy surface. Derivatives ergoˈdicity n. the quality or property of being ergodic. ΚΠ 1949 W. Feller First Berkeley Symp. Math. Statistics & Probability 418 What ergodicity might possibly mean in practice may be illustrated by the much discussed Pareto law of income distribution. 1960 G. Herdan Type-token Math. xx. 296 Under certain circumstances a system will tend in probability to a limiting form which is independent of the initial position from which it started. This is the Ergodicity Property. This entry has not yet been fully updated (first published 1972; most recently modified version published online June 2018). < adj.1928
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