A simple mathematical proof of Boltzmann's equal a priori probability hypothesis Export

@article{citeulike:4201354, abstract = {Using the Dissipation Theorem and a corollary of the Fluctuation Theorem, namely the Second Law Inequality, we give a first-principles derivation of Boltzmann's postulate of equal a priori probability in phase space for the microcanonical ensemble. We show that if the initial distribution differs from the uniform distribution over the energy hypersurface, then under very wide and commonly satisfied conditions, the initial distribution will relax to that uniform distribution. This result is somewhat analogous to the Boltzmann H-theorem but unlike that theorem, applies to dense fluids as well as dilute gases and also permits a nonmonotonic relaxation to equilibrium. We also prove that in ergodic systems the uniform (microcanonical) distribution is the only stationary, dissipationless distribution for the constant energy ensemble.}, archivePrefix = {arXiv}, author = {Evans, Denis J. and Searles, Debra J. and Williams, Stephen R.}, citeulike-article-id = {4201354}, citeulike-linkout-0 = {http://arxiv.org/abs/0903.1480}, citeulike-linkout-1 = {http://arxiv.org/pdf/0903.1480}, day = {10}, eprint = {0903.1480}, keywords = {a, boltzmanns, equal, hypothesis, priori, probability}, month = {Mar}, posted-at = {2009-03-20 20:39:08}, priority = {2}, title = {A simple mathematical proof of Boltzmann's equal a priori probability hypothesis}, url = {http://arxiv.org/abs/0903.1480}, year = {2009} }

TY - JOUR ID - citeulike:4201354 L3 - citeulike-article-id:4201354 N2 - Using the Dissipation Theorem and a corollary of the Fluctuation Theorem, namely the Second Law Inequality, we give a first-principles derivation of Boltzmann's postulate of equal a priori probability in phase space for the microcanonical ensemble. We show that if the initial distribution differs from the uniform distribution over the energy hypersurface, then under very wide and commonly satisfied conditions, the initial distribution will relax to that uniform distribution. This result is somewhat analogous to the Boltzmann H-theorem but unlike that theorem, applies to dense fluids as well as dilute gases and also permits a nonmonotonic relaxation to equilibrium. We also prove that in ergodic systems the uniform (microcanonical) distribution is the only stationary, dissipationless distribution for the constant energy ensemble. TI - A simple mathematical proof of Boltzmann's equal a priori probability hypothesis KW - a KW - boltzmanns KW - equal KW - hypothesis KW - priori KW - probability AU - Evans, Denis AU - Searles, Debra AU - Williams, Stephen PY - 2009/Mar/10/ UR - http://arxiv.org/abs/0903.1480 ER -