A higher Boltzmann distribution

@article{Catanzaro2017AHB,
  title={A higher Boltzmann distribution},
  author={Michael J. Catanzaro and V. Chernyak and J. R. Klein},
  journal={Journal of Applied and Computational Topology},
  year={2017},
  volume={1},
  pages={215-240}
}
AbstractWe characterize the classical Boltzmann distribution as the unique solution to a combinatorial Hodge theory problem in homological degree zero on a finite graph. By substituting for the graph a CW complex X and a choice of degree $$d \le \dim X$$d≤dimX, we define by direct analogy a higher dimensional Boltzmann distribution $$\rho ^B$$ρB as a certain real-valued cellular $$(d-1)$$(d-1)-cycle. We then give an explicit formula for $$\rho ^B$$ρB. We explain how these ideas relate to the… Expand
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