
110A field analysis of nonlinear irreversible thermodynamic processesFoundations of Physics 7 (1112): 907926. 1977.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…Read more

105Thermodynamics of nonlinear, interacting irreversible processes. IIFoundations of Physics 3 (1): 5388. 1973.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 va…Read more

96Thermodynamics of averaged motionFoundations of Physics 5 (4): 573589. 1975.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 a…Read more

92Concepts of stability and symmetry in irreversible thermodynamics. IFoundations of Physics 2 (23): 161179. 1972.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 symmetrydestroying external forces, the linear range may be characterized by a set of phenomenological coefficient symmetries relating coupled forces and displacements…Read more

64The underlying Brownian motion of nonrelativistic quantum mechanicsFoundations of Physics 11 (910): 653678. 1981.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 FokkerPlanck equation. The particle drift is conditioned by an auxiliary equation which is obtained through stochastic energy conservation; the logarithmic transform of…Read more

47Paths of shortest length, or geodesics, may not appear as straight lines because acceleration creates distortion. For spaces of constant curvature there are only two possibilities: Either rulers get longer as they move away from the origin or they shrink. Because the longitudinal Doppler shift corresponds to the measure of distance, in velocity space, this space is hyperbolic, corresponding to the second of the two possibilities. Transformations from one inertial frame to another are related to …Read more

40On the validity of the OnsagerMachlup postulate for nonlinear stochastic processesFoundations of Physics 9 (56): 405420. 1979.It is shown that: (i) the OnsagerMachlup 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 FokkerPlanck equation; and (iii) when the fine details of the spacetime structure of the stochastic processes are unimportant, the generalized …Read more

40The question of whether the same acceleration eld that is found in a rigid uniformly rotating disc can annul a gravitational eld is answered in the negative because their curvatures are dierent. There is an exact correspondence between a uniformly rotating disc and hyperbolic geometry of constant curvature, while, gravitational elds require nonconstant, negative curvature. The connection between the two is the freefall time; the former has constant density while the latter, constant mass. The …Read more

37Aberration and radiation pressure reflected by a moving mirror are examples of the Klein, oneway Doppler shift, and Poincare', twoway Doppler shift, disc models of hyperbolic geometry, respectively. Aberration, like the Thomas precession, is related to the angular defect, and is a kinematical eect rather than relativistic. At the angle of parallelism, determined by a stationary observer looking at a moving object in the direction normal to its motion, the rotation of the object is related to i…Read more

16Classical variational derivation and physical interpretation of Dirac's equationFoundations of Physics 17 (3): 221237. 1987.A simple random walk model has been shown by Gaveauet al. to give rise to the KleinGordon 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 pre…Read more

12Einstein's famous relation between mass and energy is interpreted in terms of the equivalence of the rate of heating of a body and the rate of increase of its inertial mass. In an adiabatic process, where the proper mass remains constant, it is the heat content, and not the energy, which is conserved because the pressure, and not the volume, is Lorentzinvariant. There are two categories of relativistic quantities: inertial and thermodynamic ones, which are transformed into one another by the wo…Read more