The Fluctuation Theorem

«In 1993 we discovered a relation, subsequently known as the Fluctuation Theorem (FT), which gives an analytical expression for the probability of observing Second Law violating dynamical fluctuations in thermostatted dissipative non-equilibrium systems. (…)

We take the assumption of causality to be axiomatic. It is causality which ultimately is responsible for breaking time reversal symmetry and which leads to the possibility of irreversible macroscopic behaviour. The Fluctuation Theorem does much more than merely prove that in large systems observed for long periods of time, the Second Law is overwhelmingly likely to be valid. The Fluctuation Theorem quantifies the probability of observing Second Law violations in small systems observed for a short time. (…)

The view that irreversibility is a result of our special place in space-time is still widely held [4]. In the present Review we will argue for an alternative, less anthropomorphic, point of view. (…)

One of the proofs of the Fluctuation Theorem given here, explicitly considers bundles of conjugate trajectory and antitrajectory pairs. (…)

In violation of the Second Law, heat energy from the surroundings can be converted into useful work to provide sufficient energy for the machine to run in reverse. This is an inescapable property of Nature which places a fundamental constraint on the operation of nanomachines. As you scale down machines they inescapably run in a mode: `two steps forward and one step back’. The ratio of forward to backward steps is given by the FT. This must also be the way that living sub-cellular organelles (machines) operate. (…)

It is logically possible that the Axiom of Causality could be replaced by its time conjugate: the Axiom of Anti-Causality. (…)

In an anticausal Universe, knowledge of its present state would enable us to predict the past but not the future.»

Denis J. Evans and Debra J. Searles, “The Fluctuation Theorem“, in Advances in Physics, 2002, Vol. 51, No. 7, 1529-1585.

 

«In other words, for a finite non-equilibrium system in a finite time, the Fluctuaction Theorem 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.»

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