Yes, there is a maximum limit to entropy and information in physics, and it is tied to the concept of the maximum entropy of a system. This limit is known as the Bekenstein bound or the holographic bound.
The Bekenstein bound arises from the interplay between gravity and entropy. According to the holographic principle, the maximum amount of information, or entropy, that can be contained within a given region of space is proportional to the surface area of that region, rather than its volume. In other words, the information content of a region is limited by the area of its boundary.
The holographic principle is a profound idea that emerged from theoretical investigations of black holes in the context of string theory. It suggests that the fundamental description of a region of space can be encoded on its boundary, much like a hologram, with the bulk of the space being derived from the boundary's information.
This bound is significant because it implies that there is a finite limit to the amount of information that can be contained within a given physical system. It provides constraints on the maximum computational capacity and storage capacity of a physical system.
The precise nature and implications of the Bekenstein bound are still subjects of ongoing research and are deeply intertwined with fundamental questions in quantum gravity and the nature of spacetime.