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The fluctuation theorem (FT), which originated from statistical mechanics, deals with the relative probability that the entropy of a system which is currently away from thermodynamic equilibrium (i.e., maximum entropy) will increase or decrease over a given amount of time. While the second law of thermodynamics predicts that the entropy of an isolated system should tend to increase until it reaches equilibrium, it became apparent after the discovery of statistical mechanics that the second law is only a statistical one, suggesting that there should always be some nonzero probability that the entropy of an isolated system might spontaneously decrease; the fluctuation theorem precisely quantifies this probability.

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  • Teorema de la fluctuació (ca)
  • Fluktuationstheorem (de)
  • Teorema sobre la fluctuación de entropía (es)
  • Fluctuation theorem (en)
  • Teorema di fluttuazione (it)
  • 요동정리 (ko)
  • ゆらぎの定理 (ja)
  • 漲落定理 (zh)
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  • El segon principi de la termodinàmica estableix, en aparent contradicció amb les equacions del moviment i dels sistemes quàntics, les quals són reversibles quant al temps, que els sistemes poden evolucionar únicament en el sentit d'incrementar l'entropia. A aquesta contradicció se l'anomena la . El teorema de la fluctuació (TF) resol aquesta "paradoxa". (ca)
  • The fluctuation theorem (FT), which originated from statistical mechanics, deals with the relative probability that the entropy of a system which is currently away from thermodynamic equilibrium (i.e., maximum entropy) will increase or decrease over a given amount of time. While the second law of thermodynamics predicts that the entropy of an isolated system should tend to increase until it reaches equilibrium, it became apparent after the discovery of statistical mechanics that the second law is only a statistical one, suggesting that there should always be some nonzero probability that the entropy of an isolated system might spontaneously decrease; the fluctuation theorem precisely quantifies this probability. (en)
  • 요동정리(搖動定理, fluctuation theorem; FT)는 통계역학에서 출발한 것으로, 열역학적 평형(i.e. 최대 엔트로피) 상태가 아닌 계의 엔트로피가 주어진 시간이 흐름에 따라 증가할지 또는 감소할지 그 상대 확률을 다루는 정리이다. 열역학 제2법칙에서 고립계의 엔트로피는 평형에 도달할 때까지 계속 증가한다고 예측하고 있으나, 제2법칙 역시 통계적 법칙임이 통계역학의 성과로 밝혀짐에 따라 고립계의 엔트로피가 자발 감소할 확률은 언제나 0이 아니어야 한다. 요동정리는 이 확률을 정량적으로 다루는 것이다. (ko)
  • ゆらぎの定理（ゆらぎのていり、英: Fluctuation Theorem, FT）とは、ある過程の実現確率と、その逆過程の実現確率との間に、対称性が存在することを示した定理である。 ゆらぎの定理は、平衡近傍に適用すると相反定理、揺動散逸定理、線形応答理論が導かれ、等温系で適用するとJarzynski等式を導くことが出来る。ゆらぎの定理は、線形応答の関係を、非線形な領域にまで拡張したものとも見ることができる。それまで有意味な関係式があると思われてこなかったような領域において発見された関係式であり、そのため発見された90年代以降、ゆらぎの定理に関係した研究は活発に行われている。 (ja)
  • Il teorema di fluttuazione (fluctuation theorem: FT) in meccanica statistica (termodinamica stocastica) verte sulla probabilità relativa che l'entropia di un sistema che si trovi attualmente lontano dall'equilibrio (stato di massima entropia) aumenti o decresca in un dato intervallo di tempo. Mentre il secondo principio della termodinamica stabilisce che l'entropia di un sistema isolato dovrebbe tendere ad aumentare fino al raggiungimento dell'equilibrio, la meccanica statistica rende evidente che questo principio ha solo valore statistico, suggerendo che ci deve essere sempre una probabilità non nulla che l'entropia di un sistema isolato decresca spontaneamente. Il teorema di fluttuazione quantifica precisamente questa probabilità. (it)
  • 漲落定理是統計力學中的一個定理，用來處理遠離熱力學平衡（熵最大值）之下，系統的熵會在某一定時間中增加或減少的相對機率。熱力學第二定律預測一獨立系統的熵應該趨向增加，直到其達到平衡為止，但在統計力學被發現之後，物理學家了解到第二定律只是統計上的一種行為，因此應該總是有一些機率會使得獨立系統的熵會自發性地減少；漲落定理準確地量化了此機率。 (zh)
  • Beim Fluktuationstheorem handelt es sich um ein Theorem aus der statistischen Physik, und zwar um eine der wenigen heutzutage bekannten exakten Relationen, die für beliebig weit aus dem Gleichgewicht getriebene Systeme gültig sind. Das Fluktuationstheorem setzt für solch ein System die Wahrscheinlichkeit von entropieerzeugenden zu entropievernichtenden Trajektorien in Beziehung. Dies ist insbesondere von Bedeutung für mikroskopisch kleine Systeme. (de)
  • El teorema de la fluctuación de entropía (TFE) o teorema de fluctuaciones, que tiene su origen en la mecánica estadística, expresa el cociente de probabilidades entre el aumento de la entropía y la disminución de la entroía, de un sistema inicialmente en equilibrio termodinámico. Dado que la entropía suele aumentar pero no se descartan situaciones en que se produzca una ligera disminución, el teorema de las fluctuaciones cuantifica esa probabilidad en términos relativos. Es decir, la entropía puede aumentar o disminuir durante un tiempo determinado, aunque lo primero es siempre más probable y el teorema dice cuanto más probable. (es)
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