A hundred years of entropy

JAN 01, 1968

From primitive machines and the discovery of fire came problems of mechanics and heat. The steam engine brought them forcibly together. Out of the study of heat‐to‐work transformations that resulted, came our entropy concept, and extension of the reasoning has brought useful applications in far‐removed subjects like probability, number theory, information theory and language.

DOI: 10.1063/1.3034744

Mahadev Dutta

PERHAPS THE PARADOX of entropy is that it has so long a history and yet so many remaining puzzles. We might say that the roots of its history go back even to primitive man. In his struggle for existence he used crude appliances and discovered fire. From closer intimacy with more and more developed machines sprang mechanics, and from fire came the theory of heat; the two were quite separate sciences.

This article is only available in PDF format

References

1. M. W. Zemansky, Heat and Thermodynamics, McGraw‐Hill, New York (1943).
2. M. Planck, Treatise on Thermodynamics, (3rd edition) Longmans, Green, London (1927).
3. E. Fermi, Thermodynamics, (Reprint of 1937 edition) Dover, New York (1956).
4. H. Zeise, Thermodynamik, Hirzel, Leipzig (1944).
5. E. A. Guggenheim, Thermodynamics, North‐Holland, Amsterdam (1950).
6. P. S. Epstein, Textbook of Thermodynamics, Wiley, New York (1937).
7. H. Poincaré, Science and Hypothesis, (Reprint of 1905 edition) Dover, New York (1953).
8. C. Carathéodory, Math. Ann. 67, 355 (1909).https://doi.org/MAANA3
9. R. Giles, Mathematical Foundations of Thermodynamics, Pergamon Press, Oxford (1964).
10. M. Born, Phys. Z. 22, 218, 249 (1921).https://doi.org/PHZTAO
11. A. Landé, p. 281 in Handbuch der Physik, Vol. 9, chap. 4, Springer‐Verlag, Berlin (1926).
12. T. Ehrenfest‐Afanassjewa, Z. Physik 93, 933 (1925).https://doi.org/ZEPYAA
13. L. Boltzmann, Wein. Ber. 53, 195 (1866);
L. Boltzmann, Pogg. Ann. 143, 211 (1871).
14. R. Clausius, Pogg. Ann. 141, 124 (1870).
15. J. J. Thompson, Applications of Dynamics to Physics and Chemistry, Macmillan, London (1884);
R. B. Lindsay, H. Margenau, Foundations of Physics, (Reprint of 1936 edition) Dover, New York (1957).
16. H. Poincaré, Thermodynamique, Gauthier‐Villars, Paris (1908).
17. P. Ehrenfest, Phys. Z. 15, 657 (1914); https://doi.org/PHZTAO
P. Ehrenfest, Ann. Physik 51, 327 (1916).https://doi.org/ANPYA2
18. M. Dutta, Statistical Physics (Foundation), World Press, Calcutta (in press).
19. L. Boltzmann, Vorlesungen über Gastheorie, (3rd edition) Barth, Leipzig (1927).
20. M. Planck, Theory of Heat Radiation, (Translation of 1914 edition) Dover, New York (1959).
21. P. Ehrenfest, Phys. Z. 15, 657 (1914).https://doi.org/PHZTAO
22. J. W. Gibbs, Elementary Principles of Statistical Mechanics, Yale U. Press, New Haven (1902).
23. S. N. Bose, Z. Physik 26, 178 (1929); https://doi.org/ZEPYAA
S. N. Bose, 27, 284 (1924).https://doi.org/ZEPYAA , Z. Phys.
24. A. Einstein, Sitzungsberichte Pruss. Acad. Wiss. p. 261 (1924);
p. 115 (1925).
25. E. Fermi, Z. Physik 48, 868 (1926); https://doi.org/ZEPYAA
P. A. M. Dirac, Proc. Roy. Soc. A112, 6660 (1926).
26. A. Einstein, Sitzungsberichte Pruss. Acad. Wiss. p. 18 (1925).
27. M. Planck, Sitzungsberichte Pruss. Acad. Wiss. p. 49, 442 (1925).
28. E. Schrödinger, Sitzungsberichte Pruss. Acad. Wiss. p. 434 (1925).
29. C. G. Darwin, R. H. Fowler, Phil. Mag. 44, 420, 823 (1922).https://doi.org/PHMAA4
30. R. H. Fowler, Statistical Mechanics, Cambridge U. Press, London (1933).
31. A. I. Khinchin, Statistical Mechanics, (Translation of 1937 edition) Dover, New York (1949).
32. A. H. Koppe, Statistical Thermodynamik, Hirzel, Leipzig (1942).
33. C. E. Shannon, Bell System Tech. J. 27, 379, 623 (1948).https://doi.org/BSTJAN
34. L. Brillouin, Science and Information Theory, (2nd edition) Academic Press, New York (1936).
35. A. I. khinchin, Mathematical Foundations of Information Theory, (Translation of 1957 edition) Dover, New York (1957).
36. R. T. Cox, The Algebra of Probable Inference, Johns Hopkins Press, Baltimore (1961).
37. S. Kullback, Information Theory and Statistics, Wiley, New York (1959).
38. G. G. Lorentz, Bull. Am. Math. Soc. 72, 903 (1966).https://doi.org/BAMOAD
39. M. Dutta, Proc. Nat. Inst. Sci. (India) 19, 1 (1953);
M. Dutta, Bull Internat. Stat. Inst. 32, 28 (1953);
M. Dutta, Proc. Nat. Inst. Sci. (India) 22, 273 (1956); https://doi.org/PIIAAP
p. 291 in Proceedings of the Summer Institute of Theoretical Physics at Mussouri, India (1959);
Jnana Oh Bijarana (in Bengali) 12, 737 (1960);
Z. Physik. Chem. (Leipzig) 228, 380 (1965).
40. M. Dutta, Indian J. Phys. 40, 422 (1966).https://doi.org/IJPYAS
41. R. A. Fisher, Statistical Theory of Estimation, California U. Press, Berkeley (1938).
42. E. T. Jaynes, Phys. Rev. 106, 20, 107 (1957); https://doi.org/PHRVAO
Statistical Physics, W. A. Benjamin, New York (1963).
43. B. Mandelbrot, Ann. Math. Stat. 33, 102 (1962).https://doi.org/AASTAD
44. M. Dutta, Sankhya A28, 391 (1966).
45. M. Dutta, S. Pal, Introduction to the Mathematical Theory of Probability and Statistics, World Press, Calcutta (1963).
46. M. Dutta, “Equivalence of Methods of Statistical Mechanics” (submitted to Indian J. Phys.).
47. G. H. Hardy, E. M. Wright, An Introduction to the Theory of Numbers, Clarendon Press, Oxford (1959).
48. M. Dutta, M. Sen, Proc. Nat. Inst. Sci. (India) A33, 66 (1967).https://doi.org/PIIAAP

More about the Authors

Mahadev Dutta. India Institute of Technology.