Entropy Changes Due to Impulses?

Classical mechanics introduces both the concepts of work and impulse i.e.: Work= F dot dr and Impulse = Fdt= dp. As we have noted previously, there seems to be a tendency in classical mechanics to focus only on the work definition which is linked to energy and time. Thus one solves Newton’s equation to find x(t) or writes a conservation of energy equation. This approach seems to be carried over into thermodynamics as the first law is written as: dE=TdS - dW. We have argued in (1) that in the case of quantum mechanics, both the impulse-momentum picture and work-energy-time picture are needed. (In particular, the one dimensional description of a photon reflecting and refracting cannot be solved without the exp(ipx) impulse scenario.) Here we suggest that the notion of entropy should also be associated with impulses. For example, consider the classical case of a particle moving in a circle with a central inward force. The kinetic energy does not change and work is zero, but the momentum vector changes and so there is an impulse. Furthermore, information changes because one needs to continuously know the momentum coordinates. We suggest that this is an example of impulse being associated with entropy. A second example we suggest is a classical particle bouncing elastically off a wall. (One may argue, however, that these notions of entropy are hand-wavy.) In the quantum world, however, we suggest that impulse plays a major role in creating entropy which is clearly defined. We suggest the example of a particle or photon with a fixed momentum passing through a tiny slit, or n-slits. In each case, one obtains a different pattern on a screen which leads to a different entropy expression. The photon or particle does not change the magnitude of its momentum i.e. there is no energy change or work, but there are impulses which are different in the various n-slit scenarios and lead to different entropies. Thus we suggest that impulses and information associated with them may lead to an increase in entropy. This suggests that the first law of thermodynamics is not a complete description of changes in entropy as it bypasses the idea of impulses and only considers work/energy changes