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Reversibility or Irreversibility? That Is the Question!
Published in Pier Luigi Gentili, Untangling Complex Systems, 2018
which is the ratio of the rate at which the system exchanges heat with the bath over its temperature. The Fluctuation Theorem defines the ratio between the probability that the small system traces a trajectory generating a positive entropy production P* (i.e., Pr(P*)) and the probability that the same small system follows the respective anti-trajectory generating a negative entropy production −P* (whose probability is Pr(−P*)). Its formulation for arbitrary averaging times is the following: [] Pr(P*)Pr(−P*)=eP*(Δt)kB.15
Kinetic equation for spatially averaged molecular dynamics
Published in Applicable Analysis, 2022
Alexander Panchenko, Kevin Cooper, Andrei Kouznetsov, Lyudmyla L. Barannyk
An accurate approximation of Q leads to an accurate approximation of the dynamics of f. However, this dynamics is not necessarily dissipative. The fluctuation theorem of Evans et al. [15] implies that the second law of thermodynamics may fail for some initial conditions. Probability of failure increases with decreasing system size. A related theorem of Galavotti and Cohen [16] guarantees dissipativity of single realization averaged over infinite time intervals under additional condition of strong chaoticity. These results allow for the possibility that a single MD trajectory has decreasing entropy production on a finite time interval. Therefore, if kinetic theory involves only spatial averaging, then it cannot be expected to be dissipative in general.
The paradigm of complex probability and Ludwig Boltzmann's entropy
Published in Systems Science & Control Engineering, 2018
The fluctuation theorem provides a mathematical justification of the second law of thermodynamics under these principles, and precisely defines the limitations of the applicability of that law for systems away from thermodynamic equilibrium.