As this relates to the human brain, and even omitting any quantum weirdness (of which there is probably a lot), all we can say is the total state of the brain at time t requires at most N bits, where N is the bound over volume of the brain. It says nothing about the (information theoretic) entropy of the _dynamics_ of the brain, which is where the process of cognition actually occurs. In fact many (if not most) physical processes have infinite entropy.
For an example of a deterministic system that exhibits such behavior, Consider the logistic map at r~5.7. There exist some coarse partitions [0] of the state space such that the trajectory that can be expressed in a finite number of bits, but this is not in general the case, even though any _given_ state of the system can be expressed in a finite number of bits. Other examples include the double pendulum, three-body orbits, and in fact most real physical systems.
In fact it is not in general true that a system with N bits of state can be always simulated with <= N bits. We can obey the Bekenstein bound without necessarily being able to simulate the process, even a complete description of the state at time t.
For the time evolution of the state space of a system, the Lyapunov Time [1] and the Lyapunov Exponent [2] are much more informative. If the time required to reach another bit of precision grows faster than polynomial time, no Turing machine can hope to simulate that physical system in a practical amount of time. In fact we also have physical bounds on how much memory we have to work with, and how fast we can flip bits for a given volume of space - simply enumerating all possible state transitions of the brain using a Turing machine will require a volume of space much larger than the brain itself if the time evolution of the system produces large Lyapynov exponents (which it absolutely does). This should come as no surprise - known NP-hard problems have the same behavior.
I would also add, even if the brain turns out to have a representation in N bits, and the state transition is (somehow) computable in polynomial time, it may still be physically infeasible to do so without just building and 'running' an actual brain.
[0]http://tcode.tcs.auckland.ac.nz/~corpus/logistic.html [1]https://en.wikipedia.org/wiki/Lyapunov_exponent [2]https://en.wikipedia.org/wiki/Lyapunov_time
PS: To me all of the above suggests that whatever the universe is doing when it's doing physics, it certainly isn't computing in the Church-Turing sense.