 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. ==statement of the fluctuation theorem== roughly, the fluctuation theorem relates to the probability distribution of the time-averaged irreversible entropy production [1], denoted \overline{\sigma}_t. the theorem states that, in systems away from equilibrium over a finite time t, the ratio between the probability that \overline{\sigma}_t takes on a value a and the probability that it takes the opposite value, &minus;a, will be exponential in at. in other words, for a finite non-equilibrium system in a finite time, the ft gives a precise mathematical expression for the probability that entropy will flow in a direction opposite to that dictated by the second law of thermodynamics. mathematically, the ft is expressed as: : \frac{\pr(\overline{\sigma}_{t}=a)}{\pr(\overline{\sigma}_{t}=-a)}=e^{at}. this means that as the time or system size increases (since \sigma is extensive), the probability of observing an entropy production opposite to that dictated by the second law of thermodynamics decreases exponentially. the ft is one of the few expressions in non-equilibrium statistical mechanics that is valid far from equilibrium. the ft was first proposed and tested using computer simulations, by denis evans, e.g.d. cohen and gary morriss in 1993 in the journal physical review letters. the first mathematical proof was given by evans and debra searles in 1994. since then, much mathematical and computational work has been done to show that the ft applies to a variety of statistical ensembles. the first laboratory experiment that verified the validity of the ft was carried out in 2002. in this experiment, a plastic bead was pulled through a solution by a laser. fluctuations in the velocity were recorded that were opposite to what the second law of thermodynamics would dictate for macroscopic systems. see wang et al. [phys rev lett, 89, 050601(2002)] and later carberry et al., [phys rev lett, 92, 140601(2004)]. this work was widely reported in the press - [http://www.newscientist.com/article/dn2572-second-law-of-thermodynamics-broken.html second law of thermodynamics &
Non-equilibrium_thermodynamics Physical_paradoxes Statistical_mechanics_theorems