A New Approach to Classical Statistical Mechanics

Nijalingappa Umakantha

.

DOI: 10.4236/jmp.2011.211153                

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.

Keywords

Statistical Equilibrium, Random Sequences, Central Limit Theorem

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	J. W. Gibbs “Elementary Principles of Statistical Mechanics,” Dever, New York, 1960 (Reprint of 1902 Edition).
[2]	R. C. Tolman, “The Principles of Statistical Mechanics,” Oxford University Press, Oxford, 1938.
[3]	D. Ter Haar, “Foundations of Statistical Mechanics,” Reviews of Modern Physics, Vol. 27, No. 3, 1955, pp. 289-338. doi:10.1103/RevModPhys.27.289
[4]	D. Chandler, “Introduction to Modern Statistical Mechanics,” Oxford University Press, Oxford, 1987.
[5]	R. von Mises, “Mathematical Theory of Probability and Statistics,” Academic Press, Waltham, 1964.
[6]	M. R. Spigel, “Theory and Problems of Probability and Statistics,” McGraw-Hill, New York, 1992.
[7]	R. Frigg, “Typicality and the Approach to Equilibrium in Boltzmann Statistical Mechanics,” Philosophy of Science, Vol. 76, No. 5, December 2009, pp. 997-1008.
[8]	J. L. Lebowitz, “Statistical Mechanics,” In: H. Stroke, Ed., The First Hundred Years, The Physical Review, AJP Publication, New York, 1995, pp. 465-471.
[9]	H. O. Georgii, “The Equivalence of Ensembles for Classical Systems of Particles,” Journal of Statistical Physics, Vol. 80, No. 5-6, 1995, pp. 1341-1378. doi:10.1007/BF02179874