In previous publications, it has been shown that entropy is a measure of the quantum-theoretic shape of the constituents of a system. In this paper, we present examples of quantum-theoretic shapes of some systems each consisting of one unit of a single constituent, in either a stable (thermodynamic) equilibrium state or in states that are not stable equilibrium. The systems that we consider are a structureless particle confined in either a linear box or a square box, and a harmonic oscillator. In general, we find that the shape of each constituent is “smooth”—without ripples—for each thermodynamic equilibrium state, and oscillatory or rippled for states that are either nonequilibrium or unstable equilibrium.
1.
Gyftopoulos, E. P., and Beretta, G. P., 1991, Thermodynamics: Foundation and Applications, Macmillan, New York.
2.
Hatsopoulos
, G. N.
, and Gyftopoulos
, E. P.
, 1976
, “A Unified Quantum Theory of Mechanics and Thermodynamics. Part I: Postulates
,” Found. Phys.
, 6
(1
), pp. 15
–31
.3.
Gyftopoulos
, E. P.
, and Cubukcu
, E.
, 1997
, “Entropy: Thermodynamic Definition and Quantum Expression
,” Phys. Rev. E
, 55
(4
), pp. 3851
–3858
.4.
Leighton, R. B., 1959, Principles of Modern Physics, McGraw-Hill, New York.
5.
Brandt, S., and Dahmen, H. D., 1995, The Picture Book of Quantum Mechanics, Springer-Verlag, New York.
6.
Slater, J., 1963, Quantum Theory of Molecules and Solids, McGraw-Hill, New York.
7.
Brandt, S., and Dahmen, H. D., op.cit., p. 106.
8.
Beretta
, G. P.
, Gyftopoulos
, E. P.
, Park
, J. L.
, and Hatsopoulos
, G. N.
, 1984
, “Quantum Thermodynamics. A New Equation of Motion for a Single Constituent of Matter
,” Nuovo Cimento
, 82B
(2
), pp. 169
–191
.9.
Hatsopoulos, G. N., and Gyftopoulos, E. P., 1979, “Thermionic Energy Conversion, Volume II: Theory, Technology, and Applications,” MIT Press, Cambridge, MA, pp. 144–145.
10.
Shankar, R., 1994, “Principles of Quantum Mechanics,” 2nd Ed., Plenum Press, New York.
11.
von Neumann, J., 1995, “Mathematical Foundations of Quantum Mechanics,” Princeton University Press, New Jersey.
12.
Brandt, S., and Dahmen, H. D., op.cit., p. 249.
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