Abstract
Terms related to gradients of scalar fields are introduced as scalar products into the formulation of entropy. A Lagrange density is then formulated by adding constraints based on known conservation laws. Applying the Lagrange formalism to the resulting Lagrange density leads to the Poisson equation of gravitation and also includes terms which are related to the curvature of space. The formalism further leads to terms possibly explaining nonlinear extensions known from modified Newtonian dynamics approaches. The article concludes with a short discussion of the presented methodology and provides an outlook on other phenomena which might be dealt with using this new approach.
Highlights
Recent work on entropic gravity by Erik Verlinde [1,2] has initiated a recovery of earlier work by the author on the thermodynamics of diffuse interfaces [3] and stimulated a generalization of this approach
When applying the Lagrange formalism, this cos2 function will eventually lead to a non-linear generalization of the Newton–Poisson equation as, for instance, that used in the modified Newtonian dynamic (MOND) approaches [19,20,21,22]
The Poisson equation of gravity (Newton’s law); a term related to curvature of space; a term introducing the mass density of vacuum; and terms related to a nonlinear generalization of the Newton–Poisson equation as used in modified
Summary
Recent work on entropic gravity by Erik Verlinde [1,2] has initiated a recovery of earlier work by the author on the thermodynamics of diffuse interfaces [3] and stimulated a generalization of this approach. The approach depicted in the present article draws on a combination of the very forceful and fundamental concepts of entropy, of the phase-field method and of the Lagrange formalism. The names of the Lagrange multipliers have been arbitrarily selected to be similar to the names of known fundamental constants, and have been assigned to the conservation law to which they are most probably related. Relations between these constants are expected to emerge from the Lagrange formalism being applied to above free energy density. Φi ( r , t) will be considered in the Lagrange density
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