Abstract
Some problems associated with the use of the maximum entropy principle, namely, (i) possible divergence of the series that is exponentiated, (ii) input-dependent asymptotic behaviour of the density function resulting from the truncation of the said series, and (iii) non-vanishing of the density function at the boundaries of a finite domain are pointed out. Prescriptions for remedying the aforesaid problems are put forward. Pilot calculations involving the ground quantum eigenenergy states of the quartic oscillator, the particle-in-a-box model, and the classical Maxwellian speed and energy distributions lend credence to our approach.
Similar content being viewed by others
References
A Shohat and J D Tamarkin, The problem of moments (American Mathematical Society, Providence, RI, 1963)
N I Akhiezer, The classical moment problem and some related questions in analysis (Oliver and Boyd, Edinburgh, 1965)
B Simon, Adv. Math. 137, 82 (1998)
A R Plastino and A Plastino, Phys. Lett. A181, 446 (1993)
Y Alhassid and R D Levine, Phys. Rev. A18, 89 (1978)
L R Mead and N Papanicolaou, J. Math. Phys. 25, 2404 (1984)
E T Jaynes, Phys. Rev. 104, 620 (1957); 108, 171 (1957)
E T Jaynes, Papers on probability, statistics and statistical physics edited by R D Rosenkrantz (Kluwer, Dordrecht, 1983)
R D Levine and M Tribus (eds), The maximum entropy formalism (MIT, Cambridge, MA, 1979)
G J Erickson and C R Smith (eds), Maximum entropy and Bayesian methods in science and engineering (Reidel, Dordrecht, 1985)
J Skilling, Maximum entropy and Bayesian methods edited by J Skilling (Kluwer, Dordrecht, 1989)
B Buck and V A Macaulay (eds) Maximum entropy in action (Clarendon Press, Oxford, 1991)
J N Kapoor, Maximum entropy models in science and engineering (Wiley Eastern, New Delhi, 1993)
I Turek, J. Phys. C21, 3251 (1988)
W H Press, S A Teukolsky, W T Vellerling and B P Flannery, Numerical recipes (Cambridge University Press, 1996)
A Wragg and D C Dowson, IEEE Trans. Inf. Theory IT-16, 226 (1970)
D C Dowson and A Wragg, IEEE Trans. Inf. Theory IT-19, 689 (1973)
A Tagliani, J Math. Phys. 34, 326 (1993); 35, 5087 (1994)
N Canosa, A Plastino and R Rossignoli, Phys. Rev. A40, 519 (1989)
M Casas, A Plastino and A Puente, Phys. Rev. A52, 949 (1995)
A R Plastino, M Casas, A Plastino and A Puente, Phys. Rev. A52, 2601 (1995)
K Banerjee, Proc. R. Soc. London 368, 155 (1979) and references therein
S N Biswas, K Datta, R P Saxena, P K Srivastava and V S Verma, Phys. Rev. D4, 3617 (1971)
H Taseli and M Demiralp, J. Phys. A21, 3903 (1988)
A K Chandra and K Bhattacharyya, Pramana — J. Phys. 43, 117 (1994)
H Meißner and E O Steinborn, Phys. Rev. A56, 1189 (1997) and references therein
R K Pathak and K Bhattacharyya, Int. J. Quant. Chem. 54, 13 (1995)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bandyopadhyay, K., Bhattacharyya, K. & Bhattacharya, A. On some problems of the maximum entropy ansatz. Pramana - J Phys 54, 365–375 (2000). https://doi.org/10.1007/s12043-000-0128-8
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s12043-000-0128-8