Statistical mechanical theory for non-equilibrium systems. IX. Stochastic molecular dynamics

Abstract

The general form for the probability density and for the transition probability of a nonequilibrium system is given. Maximization of the latter gives a generalized fluctuation-dissipation theorem by providing a molecular basis for Langevin's friction force that avoids continuum hydrodynamics. The result shows that the friction coefficient must be proportional to the variance of the stochastic equations of motion. Setting the variance to zero but keeping the friction coefficient nonzero reduces the theory to a Hoover thermostat without explicit constraint, although such a limit violates the physical requirement of proportionality between the dissipation and the fluctuation. A stochastic molecular dynamics algorithm is developed for both equilibrium and nonequilibrium systems, which is tested for steady heat flow and for a time-varying, driven Brownian particle.

Nonadiabatic excited-state molecular dynamics: Numerical tests of convergence and parameters

“…By virtue of the fluctuation-dissipation theorem derived by Langevin, the friction coefficient must be proportional to the stochastic force variance, which controls the temperature fluctuations. 76 As expected, a friction coefficient of 2.0 ps −1 provides balanced temperature coupling without the dampening effect on the dynamics associated with larger values. Our results are in good agreement with the findings of Paterlini and Ferguson 63 which demonstrated that γ in the range of 1 to 5 ps −1 is an optimum parameter for Langevin dynamics simulations in water.…”

The Interrelationship between Thermodynamics and Energetics: The True Sense of Equilibrium Thermodynamics

“…To sum up, even a brief review of the most recent literature devoted to thermodynamics and statistical physics clearly shows that we are currently confronted with a gaily coloured mixture of real concepts and traditional misconceptions -see, for example, the materials of the AIP conference entitled 'QUANTUM LIMITS TO THE SECOND LAW' [216], as well as the accompanying volume of the journal 'Entropy' containing a number of more detailed reports from that conference [217]. Meanwhile, it is truly inspiring to read serious, thoughtful work trying to overcome the persistent difficulties of the conventional thermodynamics and statistical physics [218][219][220][221]. In view of this, an attentive work with elder literature is indispensable: For sometimes we might come to the true treasuries of thoughts and notices, like the books by Prof. Dr. Peter Boas Freuchen (1866Freuchen ( -1959 [222,223].…”

Statistical mechanical theory for nonequilibrium systems. X. Nonequilibrium phase transitions

“…The claim is that the theory is completely general and encompasses all nonequilibrium systems, and a deal of quantitative evidence in support of the claim has been presented. [2][3][4][5] The theory to date has been tested for nonequilibrium phenomena for which the answer is already known from existing thermodynamic or statistical mechanical approaches. This paper addresses a class of nonequilibrium problems for which there is no accepted general theory, namely, the problem of nonequilibrium phases and the transitions between them.…”