Transient fluctuation theorems

The transient fluctuation theorem is applied to the transient response of a system. It bridges the microscopic and macroscopic domains and links the time-reversible and irreversible description of processes. In transient fluctuations, the time averages are calculated from a zero time with the known initial distribution function until a finite time. The initial distribution function may be, for example, one of the equilibrium distribution functions of statistical mechanics. So, for arbitrary averaging times, the transient fluctuation theorems are exact. The transient fluctuation theorem describes how irreversible macroscopic behavior evolves from time-reversible microscopic dynamics as either the observation time or the system size increases. It also shows how the entropy production can be related to the forward and backward dynamical randomness of the trajectories or paths of systems as characterized by the entropies per unit time. 

The transient fluctuation theorem can be derived from the probability ratio for observing a certain time-averaged value of the dissipation function that Q/ = A, and its negative that Q, = —A ... 

The fluctuation theorem deals with fluctuations. Since the statistics of fluctuations will be different in different statistical ensembles, the fluctuation theorem is a set of closely related theorems. Also some theorems consider nonequilibrium steady-state fluctuations, while others consider transient fluctuations. One of the fluctuation theorems state that in a time-reversible dynamic system in contact with constant temperature heat bath, the fluctuations in the time-averaged irreversible entropy productions in a nonequilibrium steady state satisfy Eqn (15.49) (Evans and Searles, 2002). 

Various transient or steady-state forms of Eqn (15.50) are known as integral fluctuation theorems. Fluctuation theorems express universal properties of the probability distribution p Qi) for functionals Q[x(t)], like work, heat or entropy change, evaluated along the fluctuating trajectories taken from ensembles with well-specified... 

Another advantage of the simulation is its abihty to make direct tests on the range of validity of basic thermodynamical theorems such as the fluctuation-dissipation theorem. In the second paper of the series by Evans, he considers these points for the simplest type of torque mentioned above, —X F. Consider the return to equilibrium of a dynamical variable A after taking off at r = 0 the constant torque appUed prior to this instant in time. If the torque is removed instantaneously, the first fluctuation-dissipation theorem implies that the normalized fall transient will decay with the same dependence as the autocorrelation function (A(t)A(O))- Al /(A 0)) — Therefore,... 

---