2010/02/21 by Qiuping A. Wang, Wang, Qiuping A.
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum chaos and dynamical systems #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1002.4026
52 pages
openalex publication_date 2010/02/21 · arxiv created 2010/03/26 · arxiv updated 2010/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is a general description of a probabilistic formalism of mechanics, i.e., an extension of the Newtonian mechanics principles to the systems undergoing random motion. From an analysis of the induction procedure from experimental data to the Newtonian laws, it is shown that the experimental verification of Newton law in a random motion implies a stochastic extension of the virtual work principle and the least action principle, i.e., =0 and =0 averaged over all the random paths instead of dW=0 and dA=0 for single path in regular dynamics. A probabilistic mechanics is formulated and applied to thermodynamic system. Several known results, rules and principles can be reproduced and justified from this new point of view. To mention some, we have obtain the entropy variation of the free expansion of gas and heat conduction without considering local equilibrium, and a violation of the Liouville theorem and Poincaré recurrence theorem, which allows to relate the entropy production to the work performed by random forces in nonequilibrium process.