Abstract
A number of the theorems expounded by Prigogine, Glansdorff and their collaborators are translated into electrical circuit terminology and their validity and significance discussed. The simultaneous occurrence of inductors and capacitors represents a situation not envisioned in the chemically oriented discussions and imposes some limitations. The electrical terminology also leads to “dual” theorems, in which voltage sources are replaced by current sources. The validity of the theorems in situations in which fluctuations are critical to the relaxation behavior is analyzed. The “excess entropy production” theorem is only valid if the circuit relaxation can be described by single-valued macroscopic variables, but not if it must be described by distribution functions. We stress that no purely local characterization, which examines a multistable system only in the neighborhoods where it occurs with high probability, can predict or characterize the steady state.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. Prigogine, G. Nicolis, and A. Babloyantz,Phys. Today 25(11):23 (1972).
K. J. McNeil and D. F. Walls,J. Stat. Phys. 10:439 (1974).
R. Landauer,J. Appl. Phys. 33:2209 (1962).
R. Landauer,J. Stat. Phys. 9:351 (1973);11:525 (1974).
F. Schlögl,Z. Physik 191:81 (1966).
F. Schiögl,Z. Physik 243:303 (1971).
F. Schlögl,Z. Physik 248:446 (1971).
R. Landauer,IBM J. Res. Develop. 1:223 (1957).
H. Busch,Stabilität, Labilität, und Pendelungen in der Elektrotechnik, S. Hirzel, Leipzig (1913).
P. Glansdorff and I. Prigogine,Thermodynamic Theory of Structure Stability and Fluctuations, Wiley-Interscience, New York (1971).
J. M. Ziman,Can. J. Phys. 34:1256 (1956).
J. B. Keller,J. Math. Phys. 11:2919 (1970).
J. H. Jeans,The Mathematical Theory of Electricity and Magnetism, 5th ed., Cambridge (1951).
R. Landauer, Inadequacy of entropy and entropy derivatives in characterizing the steady state,Phys. Rev. A, to be published.
S. R. de Groot and P. Mazur,Non-Equilibrium Thermodynamics, North-Holland, Amsterdam (1961), p. 45.
G. Nicolis, inAdvances in Chemical Physics, Vol XIX, I. Prigogine and S. Rice, eds., Wiley-Interscience, New York (1971).
I. Prigogine,Introduction to Thermodynamics of Irreversible Processes, 3rd ed., Wiley-Interscience, New York (1967), Chapter VI.
R. Landauer and J. W. F. Woo,Comm. Solid State Phys. 4:139 (1972).
J. W. F. Woo and R. Landauer,IEEE J. Quantum Electron. QE-7:435 (1971).
H. K. Janssen,Z. Physik 270:67 (1974).
I. Matheson, D. F. Walls, and C. W. Gardiner,J. Stat. Phys. 12:21 (1975).
H. Haken,Phys. Lett. 46A:443 (1973).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Landauer, R. Stability and entropy production in electrical circuits. J Stat Phys 13, 1–16 (1975). https://doi.org/10.1007/BF01012596
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01012596