arXiv:physics/0209066v1 [physics.class-ph] 18 Sep 2002 Europhysics Letters PREPRINT An Information-Theoretic formulation of the Newton’s Second Law Mario J. Pinheiro Department of Physics and Centro de Fisica dos Plasmas, Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal PACS. 02.30.Xx – Calculus of variations. PACS. 02.50.Cw – Probability theory. PACS. 05.20.-y – Classical statistical mechanics. Abstract. – From the principle of maximum entropy for a closed system in thermal equi- librium, 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 thermody- namical 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 E i ,  p i and  L i , all constituted of particles of a single species of mass m. The internal energy U i of each subsystem moving with momentum − → p i in a Galilean frame of reference is given by E i = U i + − → p 2 i 2m +  L 2 i 2I i . (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  i S i  E i − p 2 i 2m − L 2 i 2I i  . (2) c  EDP Sciences