Abstract
A modification of the thermodynamic Weinhold metric is introduced by the statistical scheme of bit-number cumulants discussed in earlier papers. It is a metric in the space of intensive thermal variables and becomes identical with the Weinhold metric if transformed into the space of extensive variables. The quadratic forms of the metric tensor are different for finite distances. The here presented metric is signified by quantities defined in general statistics, distinguished by important invariance properties and moreover it brings simplifications.
Similar content being viewed by others
References
Weinhold, F.: J. Chem. Phys.63, 2479 (1975);63, 2482 (1975);63, 2488 (1975);63, 2496 (1975);65, 559 (1976)
Salamon, P., Andresen, B., Gait, P.D., Berry, R.S.: J. Chem. Phys.73, 1001 (1980)
Salamon, P., Berry, R.S.: Phys. Rev. Lett.51, 1127 (1983)
Rupeiner, G.: Phys. Rev. A20, 1608 (1979);24, 488 (1981);27, 1116 (1983); Phys. Rev. Lett.50, 287 (1983)
Salamon, P., Nulton, J., Ihrig, E.: J. Chem. Phys.80, 436 (1984)
Nulton, J., Salamon, P., Andresen, B., Qi Anmin: Quasistatic processes as step equilibrations. J. Chem. Phys. (submitted for publication)
Nulton, J., Salamon, P.: The geometry of the ideal gas. Phys. Rev. A (to appear)
Feldmann, T., Andresen, B., Anmin Qi, Salamon, P.: Thermodynamic lengths and intrinsic time scales in molecular relaxation. (draft) San Diego State University.
Salamon, P., Nulton, J.D., Berry, R.S.: Length in statistical thermodynamics. J. Chem. Phys. (to appear)
Flick, J.D., Salamon, P., Andresen, B.: Metric bounds on losses in adaptive coding. I.E.E.E. Transact. Inf. Theor. (submitted for publication)
Schlögl, F.: Z. Phys. B — Condensed Matter20, 177 (1975);22, 301 (1975);52, 51 (1983); Phys. Rep.62, 267 (1980)
Jaynes E.T.: Phys. Rev.106, 620 (1957)
Kullback, S.: Ann. Math. Stat.22, 79 (1951); Information theory and statistics. New York: Wiley 1951
Schlögl, F.: Z. Phys.191, 81 (1966);198, 560 (1967)
Salamon, P., Nulton, J., Feldmann, T., Andresen, B.: Relaxation times and metric bounds on dissipation (draft). San Diego State University
Hatsopoulos, G.N., Keeman, J.H.: Principles of general thermodynamics. New York: J. Wiley 1965
Schlögl, F.: Z. Phys.191, 81 (1966);198, 559 (1967);249, 1 (1971)
Schlögl, F.: Z. Phys.244, 199 (1971);248, 446 (1971);249, 1 (1971); Phys. Lett.26A, 193 (1971); Progr. Theor. Phys. Suppl.64, 100 (1978); Z. Phys. B — Condensed Matter33, 199 (1979)
Ruppeiner, G.: Phys. Rev. A27, 1116 (1983)
Glansdorff, P., Prigogine, I.: Physica46, 344 (1970)
Schlögl, F.: Z. Phys.243, 303 (1971); Thermodynamics and regulation of biological processes. Lamprecht, L., Zotin, A.I., (eds.). Berlin, New York: de Gruyter, 1985
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Schlögl, F. Thermodynamic metric and stochastic measures. Z. Physik B - Condensed Matter 59, 449–454 (1985). https://doi.org/10.1007/BF01328857
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01328857