Thursday, December 13, 2007

Though The Disorder a Blog Was Born

I was thinking the other day about entropy and I was wondering if there was a static solution to the climatic temperature as a function of greenhouse gases based on the principle of maximum entropy. That thought inspired me to create this blog. The blog title represents the order that I hope to find in the Chaos.

The blog will contain my random thoughts which will explore the question of weather statistical mechanics may be more useful in understanding the climate then fluid dynamics. The laws of Fluid mechanics are valid when the intrinsic properties of the fluid change slowly relative to the mean free path of the particles in the fluid.

In the case of the climate all energy must inevitableness leave the earth through radiation. Photons effect the intrinsic properties of a fluid but our ability to measure fluid properties is on much smaller scales then the distance that light travels before interacting with the fluid. While we could try to treat the two systems as separate, photons behave like particles in the sense that they can collide with molecules and exchange energy trough collisions.

Because the mean free path of photons is much larger then molecules the distribution of photons my suggest a different temperature then the distribution of particles. Moreover when the particles absorb select frequencies of photons the distribution of photons is no longer a black body distribution and the distribution of particle is likely no longer a perfect Boltzmann distribution. If the particle distribution is altered from an idealized distributionby the photons then what consequence will this have on thermodynamic properties like, conductivity, viscosity and entropy.

To try to answer the question my thought was that more fundamental principles are required to properly understand the interaction between light and matter on a statistical level. The Boltzmann distribution is derived based on the assumption that the only thing which effects the probability of a given state is the energy of that state, the number of total states and the total energy in the system.

Rather then make assumptions about the probability of a given state we can consider the dymanics between the states. We express the dynamics as a state transition matrix. The elements in the matrix are based on the probability of a transition from one state to another state within a given period of time. The equilibrium of the system is when for each and every state the probability of a particle transitioning from one state to another is equal to the probability a particle transitioning from another state to that state.

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