Freiburg 2008 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 5: Vielteilchentheorie

MP 5.3: Talk

Tuesday, March 4, 2008, 17:40–18:00, KGI-HS 1023

A statistical mechanical analogue of the second law: The increase of entropy upon release of a constraint in classical systems. — •Jürgen Schlitter — Lehrstuhl für Biophysik, Ruhr-Universität Bochum, Deutschland

Computer simulations have drawn new attention to holonomic constraints being used for simplified calculations, and also for maintaining and parameterizing equilibrium states. Second-law like phenomena of relaxation and equilibration are familiar to computational physicists. Their analysis has been facilitated by methods for calculating thermodynamic potentials which now enable a new approach to the formal foundation of the observed behavior. Here, we first consider classical mechanical systems which are fixed in a conditional equilibrium by means of constraints. If there are mean forces under this condition, they are shown to be purely entropic. Next, spontaneous transitions at constant energy are considered which occur upon release of a constraint. For any such transition it is shown that it leads on average to a region of higher entropy in phase space. This is a formally derived analogue of the second law of thermodynamics. Examples of constrained systems are given which show the range of application of this approach. The result is discussed with respect to a seeming contradiction to time symmetry. The latter manifests itself by the occurrence of residual fluctuations. It is not violated during the formal derivation, but by the underlying experimental setup. Entropy is only measured at equilibrium. The two-step mode of release and constraint is essential for the formal result. Reference: J. Schlitter, Mol. Phys. 104: 2829-2834, 2006