1. Reversible Computation Avraham Guttman Topics in Biological Physics Prof. Elisha Moses, Dr. Roy Bar-Ziv R. Landauer, IBM J. Res. Dev. 3, 183 (1961) Bennett, C. H., IBM J. Res. Dev. 17, 525 (1973) R. Landauer, Physica Scripta. Vol. 35, 88-95, 1987 Feynman, Lectures on Computation, 1999

2. Reversible Computation - Outline Thermodynamic Reversibility Physics of Logic Reversibility mRNA Transcription 1 0 0 1 T

3. Memory Tape 0100

4. Single Bit Operation 1 0 0 1

5. Carnot Engine http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/carnot.htm

6. Carnot Cycle Thermodynamically Reversible

7. AND - Irreversible gate Loss of Information

8. T Physically Loss of Information 0 1 Loss offree energy

9. von Neumann – Landauer Limit In each irreversible bit operation:

10. Information Erasure ErasureIrreversible Process Infinite tape: No need for erasure Nonphysical For N erased bits: Loss of energy

11. Physical Reversible Copy X Copier Model

12. Bennetts’ Three-Tape Reversible Computation 1.Algorithm steps while saving 2.Copying the output 3.Retracing the algorithm steps 101010101010101010 000000000000000000 000000000000000000 Standard History Copy R3R3 R2R2 R1R1 R 1 -1 R 2 -1 R 3 -1 1 R1R1 0 R2R2 1 R3R3 011110101010101010

13. mRNA Transcription from DNA to protein

14. mRNA Transcription from DNA to protein RNA (N bases) +X-S-P-P-PRNA (N+1 bases) +P-P i =G,C,A,U (Triphosphate)(Pyrophosphate) Transistor:

15. Reversible Computation - Outline Thermodynamic Reversibility Physics of Logic Reversibility mRNA Transcription 1 0 0 1 T Thank You