On an Unusual Quantization Procedure of Heat Conduction

We have shown in our previous works how to introduce the quantization procedure into the theory of heat conduction. In the present paper we point out where and why we need to complete the previous results to obtain the Hamiltonian by which we can bring 'zero point' energy into the theory of thermal field. We calculate the energy and the quasi-particle number operator for heat conduction.

[1]  R. Kotowski.  On the lagrange functional for dissipative processes , 1989 .

[2]  P. Rosen.  On Variational Principles for Irreversible Processes , 1953 .

[3]  István Gyarmati,et al.  Non-equilibrium Thermodynamics , 1970 .

[4]  Lars Onsager,et al.  Fluctuations and Irreversible Processes , 1953 .

[5]  P. Morse,et al.  Methods of theoretical physics , 1955 .

[6]  A. R. P. Rau,et al.  A unified formulation of the construction of variational principles , 1983 .

[7]  Lars Onsager,et al.  Fluctuations and Irreversible Process. II. Systems with Kinetic Energy , 1953 .

[8]  S. Sieniutycz,et al.  Variational and extremum properties of homogeneous chemical kinetics. II. Minimum dissipation approaches , 1992 .

[9]  K. Martinás,et al.  Examination of phenomenological coefficient matrices within the canonical model of field theory of thermodynamics , 1997 .

[10]  S. K. Ratkje,et al.  Perturbational thermodynamics of coupled electrochemical heat and mass transfer , 1996 .

[11]  B. Finlayson.  The method of weighted residuals and variational principles : with application in fluid mechanics, heat and mass transfer , 1972 .

[12]  Berry,et al.  Canonical formalism, fundamental equation, and generalized thermomechanics for irreversible fluids with heat transfer. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  F. Márkus,et al.  Hamilton-Lagrange formalism of nonequilibrium thermodynamics. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  Berry,et al.  Least-entropy generation: Variational principle of Onsager's type for transient hyperbolic heat and mass transfer. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[15]  W. Muschik,et al.  Structure of variational principles in nonequilibrium thermodynamics. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  P. Glansdorff,et al.  Thermodynamic theory of structure, stability and fluctuations , 1971 .

[17]  R. Courant,et al.  Methods of Mathematical Physics , 1962 .

[18]  József Verhás,et al.  Thermodynamics and Rheology , 1997 .

[19]  S. K. Ratkje,et al.  Variational principle for entropy in electrochemical transport phenomena , 1996 .

[20]  P. Dirac.  Principles of Quantum Mechanics , 1982 .

[21]  A. Messiah.  Quantum Mechanics , 1961 .

[22]  Maurice A. Biot,et al.  Variational principles in heat transfer , 1970 .

[23]  Stanislaw Sieniutycz.  Conservation Laws in Variational Thermo-Hydrodynamics , 1994 .

[24]  I. Gyarmati.  On the Wave Approach of Thermodynamics and some Problems of Non-Linear Theories , 1977 .

[25]  D. Jou,et al.  A Hamiltonian formulation for two hierarchies of thermodynamic evolution equations , 1991 .

[26]  F. Márkus,et al.  A Variational Principle in Thermodynamics , 1991 .

[27]  J. Linnett,et al.  Quantum mechanics , 1975, Nature.

[28]  I. Prigogine.  Etude thermodynamique des phénomènes irréversibles , 1947 .

[29]  G. Lebon,et al.  Hamiltonian Extended Thermodynamics , 1990 .

[30]  Berry,et al.  Conservation laws from Hamilton's principle for nonlocal thermodynamic equilibrium fluids with heat flow. , 1989, Physical review. A, General physics.

[31]  K. Anthony.  Phenomenological thermodynamics of irreversible processes within Lagrange formalism , 1990 .

[32]  On the Construction of Potentials and Variational Principles in Thermodynamics and Physics , 1991 .

[33]  L. W.,et al.  The Theory of Sound , 1898, Nature.

[34]  F. Vázquez,et al.  Path integral approach to fluctuations in relativistic transport , 1998 .