An Information-Theoretic formulation of the Newton’s Second Law

– From the principle of maximum entropy for a closed system in thermal equilibrium, it is shown for the first instance, to exist a clear relation between total entropy S (in terms of arrangements of particles) and the classical expression for the force acting on a particle in a rotating frame. We determine relationships between arrangement of particles and force in the case of the gravitational and elastic forces. Introduction. – The notion of entropic force has been successfully applied to an increasing number of problems, e.g., to the calculation of forces acting at the ends of a single Gaussian macromolecule [1], the evocation of the geometric features of a surface as creating entropic force fields [2], and the attractive Coulomb force between defects of opposite type [3]. The purpose of the present paper is to present a new and unusual procedure, using a thermodynamical and mechanical framework, to obtain the (entropic) force acting over a particle in a rotating frame in terms of arrangement of particles. Extremum Principle. – As is known, from Liouville theorem it is deduced the existence of seven independent additives integrals: the energy, 3 components of the linear momentum ~ p and 3 components of the angular momentum ~ L. Let us consider an isolated macroscopic system S composed by N infinitesimal macroscopic subsystems S (with an internal structure possessing a great number of degrees of freedom, allowing the definition of an entropy) with Ei, ~ pi and ~ Li, all constituted of particles of a single species of mass m. The internal energy Ui of each subsystem moving with momentum −→p i in a Galilean frame of reference is given by Ei = Ui + −→p i 2m + ~ Li 2Ii . (1) The entropy of the system is the sum of the entropy of each subsystems (and function of the their internal energy U , S = S(U)): S = N