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  1.  79
    Concepts of Stability and Symmetry in Irreversible Thermodynamics. I.B. H. Lavenda - 1972 - Foundations of Physics 2 (2-3):161-179.
    Concepts of stability and symmetry in irreversible thermodynamics are developed through the analysis of system energy flows. The excess power function, derived from a local energy conservation equation, is shown to yield necessary and sufficient stability criteria for linear and nonlinear irreversible processes. In the absence of symmetry-destroying external forces, the linear range may be characterized by a set of phenomenological coefficient symmetries relating coupled forces and displacements, velocities, and accelerations, whereas rotational phenomena in nonlinear processes may be characterized by (...)
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  2.  79
    Thermodynamics of Nonlinear, Interacting Irreversible Processes. II.B. H. Lavenda - 1973 - Foundations of Physics 3 (1):53-88.
    The scope of the thermodynamic theory of nonlinear irreversible processes is widened to include the nonlinear stability analysis of system motion. The emphasis is shifted from the analysis of instantaneous energy flows to that of the average work performed by periodic nonlinear processes. The principle of virtual work separates dissipative and conservative forces. The vanishing of the work of conservative forces determines the natural period of oscillation. Stability is then determined by the variations of the dissipative forces with amplitude of (...)
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  3.  93
    A Field Analysis of Nonlinear Irreversible Thermodynamic Processes.B. H. Lavenda - 1977 - Foundations of Physics 7 (11-12):907-926.
    The generalized thermodynamic potential analysis of nonlinear irreversible processes precludes the analysis of rotational processes. The nonexistence of scalar potential functions necessitates a thermodynamic analysis of the system forces. A field analysis in the phase space of the generalized displacements and velocities treats the force components as tensors of second order that tend to deform and rotate the irreversible process, which is viewed as an elastic material. The analysis of chemical oscillatory processes involves the introduction of the thermodynamic vector potential, (...)
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  4.  89
    Thermodynamics of Averaged Motion.B. H. Lavenda - 1975 - Foundations of Physics 5 (4):573-589.
    The thermodynamics of averaged motion treats the asymptotic spatiotemporal evolution of nonlinear irreversible processes. Dissipative and conservative actions are associated with short and long spatiotemporal scales, respectively. The motion of asymptotically stable systems is slow, monotonic, and continuous, so that the microscopic state variable description of rapid motion can be supplanted by an analysis of the macroscopic variable equations of motion of amplitude and phase. Rapid motion is associated with instability, and the direction of system motion is determined by thermodynamic (...)
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  5.  45
    The Underlying Brownian Motion of Nonrelativistic Quantum Mechanics.E. Santamato & B. H. Lavenda - 1981 - Foundations of Physics 11 (9-10):653-678.
    Nonrelativistic quantum mechanics can be derived from real Markov diffusion processes by extending the concept of probability measure to the complex domain. This appears as the only natural way of introducing formally classical probabilistic concepts into quantum mechanics. To every quantum state there is a corresponding complex Fokker-Planck equation. The particle drift is conditioned by an auxiliary equation which is obtained through stochastic energy conservation; the logarithmic transform of this equation is the Schrödinger equation. To every quantum mechanical operator there (...)
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  6.  25
    On the Validity of the Onsager-Machlup Postulate for Nonlinear Stochastic Processes.B. H. Lavenda - 1979 - Foundations of Physics 9 (5-6):405-420.
    It is shown that: (i) the Onsager-Machlup postulate applies to nonlinear stochastic processes over a time scale that, while being much longer than the correlation times of the random forces, is still much shorter than the time it takes for the nonlinear distortion to become visible; (ii) these are also the conditions for the validity of the generalized Fokker-Planck equation; and (iii) when the fine details of the space-time structure of the stochastic processes are unimportant, the generalized Fokker-Planck equation can (...)
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  7.  11
    Classical Variational Derivation and Physical Interpretation of Dirac's Equation.B. H. Lavenda - 1987 - Foundations of Physics 17 (3):221-237.
    A simple random walk model has been shown by Gaveauet al. to give rise to the Klein-Gordon equation under analytic continuation. This absolutely most probable path implies that the components of the Dirac wave function have a common phase; the influence of spin on the motion is neglected. There is a nonclassical path of relative maximum likelihood which satisfies the constraint that the probability density coincide with the quantum mechanical definition. In three space dimensions, and in the presence of electromagnetic (...)
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