4 p3 it is possible to construct macroscopic

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Unformatted text preview: tion of information is bounded: No action at a distance. ¶3. P2. The amount of information which can be encoded in the state of a finite system is bounded: This is a consequence of thermodynamics and quantum theory. ¶4. P3. It is possible to construct macroscopic, dissipative physical devices which perform in a recognizable and reliable way the logical functions AND, NOT, and FAN-OUT: This is an empirical fact. C. REVERSIBLE COMPUTING C.2.b 53 Conservative logic ¶1. “Computation is based on the storage, transmission, and processing of discrete signals.” ¶2. Only macroscopic systems are irreversible, so as we go to the microscopic level, we need to understand reversible logic. This leads to new physical principles. ¶3. P4. Identity of transmission and storage: In a relativistic sense, they are identical. ¶4. P5. Reversibility: Because microscopic physics is reversible. ¶5. P6. One-to-one composition: Physically, fan-out is not trivial, so we cannot assume that one function output can be substituted for any number of input variables. We have to treat fan-out as a specific signal-processing element. ¶6. P7. Conservation of additive quantities: It can be shown that in a reversible systems there are a number of independent conserved quantities. ¶7. In many systems they are additive over the subsystems. ¶8. P8. The topology of space-time is locally Euclidean: “Intuitively, the amount of ‘room’ available as one moves away from a certain point in space increases as a power (rather than as an exponential) of the distance from that point, thus severely limiting the connectivity of a circuit.” ¶9. What are su cient primitives for conservative computation? The unit wire and the Fredkin gate. C.3 Unit wire ¶1. Information storage in one reference frame may be information transmission in another. E.g., leaving a note on a table in an airplane (at rest with respect to earth or not, or to sun, etc.). (and at its output at an analogous called the state ofathe wiresignal-processing primitive, namely, the Fredkin conservative logic, time t + 1) is role is played by si...
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