Relative entropy, topological pressure and variational principle for locally compact sofic group actions

2025/11/24 by Li, Xianqiang, Liu, Zhuowei
Mathematics · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Mathematical Dynamics and Fractals

paper · doi:10.48550/arxiv.2511.19086

Abstract

For a locally compact sofic group continuously acting on a compact metric space, we first study the relative sofic entropy and prove an additive inequality relating sofic entropy and relative sofic entropy. Moreover, it is shown that the relative variational principle remains valid in this paper. Secondly, the topological pressure for locally compact sofic group actions is investigated and the variational principle for topological pressure in this sofic context is established. As an application, we show a sufficient condition for a signed measure to be a G-invariant measure. These contributions generalize the classical results for countable sofic groups on such spaces.

Citations

• Locally compact sofic entropy theory
• Locally compact sofic groups
• Relative entropy and the Pinsker product formula for sofic groups
• Topological pressure and the variational principle for actions of sofic groups
• Measure conjugacy invariants for actions of countable sofic groups

Related

• Locally compact sofic entropy theory
• Local variational principle concerning entropy of a sofic group action
• Topological pressure and the variational principle for actions of sofic groups
• Sofic entropy, after Lewis Bowen, David Kerr and Hanfeng Li
• Local and doubly empirical convergence and the entropy of algebraic actions of sofic Groups