Heat has a kinetic term in overdamped stochastic thermodynamics

Abstract

In the derivation of the thermodynamics of overdamped systems, one ignores the kinetic term contribution, since the velocity is a slow variable to the forces. In this paper, we show that the kinetic term needs to be present in the calculation of the heat distribution in order to have a correct correspondence between the underdamped and overdamped cases, meaning that the velocity can not be fully ignored in the thermodynamics of these systems. We emphasize the result for two different systems, the harmonic potential, and the logarithm potential.

Probabilities for informational free lunches in stochastic thermodynamics

“…For the sake of simplicity, we skip the kinetic energy in the heat. Nonetheless, it must be emphasized that the kinetic energy needs to be present in the heat formula even for overdamped systems [27]. That kinetic energy correction in an experiment is very small, thus scrapping it does not significantly alter the results.…”