The Variational Principle for Entropy of Countable State Shift Spaces with Specification

Authors

  • Alex Paschal University of North Carolina at Chapel Hill
  • Amy Somers University of California, Santa Barbara

DOI:

https://doi.org/10.46787/pump.v9i.6390

Keywords:

countable-state shift spaces; variational principle; Gurevich entropy; specification property; thermodynamic formalism

Abstract

We generalize the well-studied specification property to countable-state shift spaces. We present an infinite class of examples of such spaces. Using a generalized notion of Gurevich entropy, we prove the variational principle for these spaces. This lays the foundation for developing the theory of equilibrium states in this setting.

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Published

2026-01-24

How to Cite

Paschal, A., & Somers, A. (2026). The Variational Principle for Entropy of Countable State Shift Spaces with Specification. The PUMP Journal of Undergraduate Research, 9, 30–42. https://doi.org/10.46787/pump.v9i.6390

Issue

Vol. 9 (2026): PUMP Journal of Undergraduate Research

Section

Articles

License

Copyright (c) 2026 Alex Paschal, Amy Somers

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

The author(s) will retain the copyright, but by submitting the article agree to grant permission to the PUMP Journal of Undergraduate Research to publish, distribute, and archive the article. The author(s) will acknowledge prior publication in the PUMP Journal of Undergraduate Research for all future uses of the article or parts of it.