Statistical mechanics of phase–space curves

Abstract

We study the classical statistical mechanics of a phase-space curve.This unveils a mechanism that, via the associated entropic force, provides us with a simple realization of effects such as confinement, hard core, and asymptotic freedom. Additionally, we obtain negative specific heats, a distinctive feature of self-gravitating systems and negative pressures, typical of dark energy.

3D effects of the entropic force

“…This picture can be always arrived at after an adequate coordinates-change [1]. If we take into account that a) the integrands are exact differentials and b) the integrals are independent of the curve's shape and only depend on their end-points q 0 1 , we deduce i) For the partition function…”

“…A previous one-dimensional study concerning the classical statistical mechanics of arbitrary phase-space curves Γ [1] was shown to uncover some strange (for a classical setting), like confinement and asymptotic freedom. Of course, by confinement one alludes to the physical phenomenon that impedes isolation of color charged particles (such as quarks), that cannot be isolated singularly, while asymptotic freedom is a property of some gauge theories that originates bonds between particles to become asymptotically weaker as distance decreases.…”

“…We recapitulate here the formalism expounded in [1] and consider a typical, n-dimensional harmonic oscillator-like Hamiltonian in thermal contact with a heat-bath at the inverse temperature β (that will be kept constant throughout).…”

“…As in [1], we consider curves, parameterized as a function of the independent variable q 1 , passing through the origin, for which we have p(0) = 0 and q(0) = 0, and, thus, for any temperature T , U(0, 0) = 0. This picture can be always arrived at after an adequate coordinates-change [1].…”

“…In [1] only the one-dimensional case was considered in detail. In particular, we emphasize that we treat the entropic forces in three-dimensional fashion.…”