Acceleration of particles in an isotropic random force field

TL;DR

This paper demonstrates that particles immersed in an isotropic random force field tend to gain energy over many interactions, due to the higher probability of energy gain compared to loss in each interaction.

Contribution

It provides a probabilistic analysis showing that particles generally gain energy in isotropic random force fields, highlighting a fundamental energy transfer mechanism.

Findings

Particles tend to gain energy after many interactions.

Probability of energy gain exceeds that of energy loss in isotropic fields.

Energy gain probability depends on impulse and initial momentum.

Abstract

If we have a particle immersed in a field of random forces, each interaction of the particle with the field can enlarge or diminish its kinetic energy. In this work is shown that in general, for any field of random force with uniform distribution of directions, the probability to gain kinetic energy is larger that the probability to lose it. Therefore, if the particle is submitted to a great number of interactions with the force stochastic field, the final result will be that the particle will gain energy. The probability to gain energy in each interaction is Pg=1/2 (1+T/(2Po)), where T is the impulse given by the field and Po is the momentum of the particle before the interaction. The probability to lose energy in each interaction is Pl=1/2 (1-T/(2Po)).