Pressure for the space of average pseudo-orbits with block sub-additive potentials

In this paper, we introduce the concept of block sub-additive potential. The topological and measure-theoretic pressures are then defined for the space of average pseudo-orbits relative to any block sub-additive potential and any open cover of a given compact metric space. A local variational principle connecting these pressures is established, and it is further proven that they are equivalent to the corresponding topological and measure-theoretic pressure (in the ergodic case), respectively, defined for the induced sub-additive potential and the specified open cover. Additionally, the global versions of these concepts are also investigated, and a result that bridges the global and local perspectives is presented.