# Complexity Explorer Santa Fe Institute ## Introduction to Renormalization

• Introduction
• Coarse graining Alice and Dinah
• Coarse graining part I - Clustering algorithms
• Coarse graining part II - Entropy
• Markov Chains
• Mathematics of coarse grained Markov chains
• Mathematics of Coarse grained Markov Chains: The General Case
• A puzzle: origin of the slippy counter
• Where we are so far
• Cellular Automata: Introduction
• Israeli and Goldenfeld; projection and commuting diagrams
• Networks of Renormalization
• Coarse-graining the Lattice
• From Quantum Electrodynamics to Plasma Physics
• Conclusion: Keeping the things that matter
• Homework

#### 6.2 The Thermal Physics of Plasma » Quiz Solution

How do we describe a plasma in thermal equilibrium?

A. the density of particles at any point depends upon (a) the local electric potential, (b) the number of particles of the opposite charge nearby.
B. the density of particular at any point depends upon (a) the number of particles of the same charge nearby, and (b) the system temperature.
C. the density of particular at any point depends upon (a) the number of particles of the same charge nearby, and (b) the number of particles of the opposite charge nearby.
D. the density of particles at any point depends upon (a) the local electric potential, (b) the system temperature.

Answer (D). It of course matters where the other particles are; so in one sense all four answers are correct if we're talking about correlations. But the question is about how we actually choose to describe all the correlations in the system: what quantities go into the function? It turns out that the trick to solving this problem is to summarize the information about the positions of all the other particles using the electric potential. This tells you the cumulative effect of where everything is on a test particle. The temperature then tells you how much the test particles care about being in a very high or very low energy state.