  While Landauer's Principle sets a lower bound for the work required for a
computation, that work is recoverable for efficient computations. However,
practical physical computers, such as modern digital computers or biochemical
systems, are subject to constraints that make them inefficient -- irreversibly
dissipating significant energy. Recent results show that the dissipation in
such systems is bounded by the nonreciprocity of the embedded computation. We
investigate the consequences of this bound for different types of memory,
showing that different memory devices are better suited for different
computations. This correspondence comes from the time-reversal symmetries of
the memory, which depend on whether information is stored positionally or
magnetically. This establishes that the time symmetries of the memory device
play an essential roll in determining energetics. The energetic consequences of
time symmetries are particularly pronounced in nearly deterministic
computations, where the cost of computing diverges as minus log of the error
rate. We identify the coefficient of that divergence as the dissipation
divergence. We find that the dissipation divergence may be zero for a
computation when implemented in one type of memory while it's maximal when
implemented with another. Given flexibility in the type of memory, the
dissipation divergence is bounded below by the average state compression of the
computation. Moreover, we show how to explicitly construct the memory to
achieve this minimal dissipation. As a result, we find that logically
reversible computations are indeed thermodynamically efficient, but logical
irreversibility comes at a much higher cost than previously anticipated.
