Abstract
A new approach to classical statistical mechanics is presented; this is based on a new method of specifying the possible “states” of the systems of a statistical assembly and on the relative frequency interpretation of probability. This approach is free from the concept of ensemble, the ergodic hypothesis, and the assumption of equal a priori probabilities.
Highlights
The object of classical statistical mechanics is to explain the properties of an assembly of a large number of identical particles in terms of the laws of classical mechanics
A new approach to classical statistical mechanics is presented; this is based on a new method of specifying the possible “states” of the systems of a statistical assembly and on the relative frequency interpretation of probability
The theory presented by Tolman and the subsequent authors [3,4] is based on: 1) the concept of “state” of a many-particle system as defined by classical mechanics in the sense that the state of a N-particle system at any instant of time can be specified by a point in 6N dimensional phase space and 2) the notion of probability prevalent at the beginning of the last century according to which probability refers to a manyparticle system “chosen at random from the ensemble” of many-particle systems
Summary
The object of classical statistical mechanics is to explain the (statistical) properties of an assembly of a large number of identical particles in terms of the (deterministic) laws of classical mechanics Such a theory has been developed by Gibbs in the first decade of the last century [1]. In this paper we present a new approach to classical statistical mechanics based on the significant progress made during and after the third decade of the last century in the theory of probability (a branch of pure mathematics) and the methods of statistical analysis (a branch of applied mathematics) [5,6] This new approach is based on: 1) a new method of specifying the possible “states” of an assembly of particles which (method) is consistent with the requirements of statistical analysis, and 2) on the relative frequency interpretation of probability. For the sake of clarity, the distinctive features of the two approaches are discussed in the text
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
