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Overview of the Derivations

In this paper I derive a formula that relates energy to information in the context of molecular machines. Before the formula can be derived, it is necessary to define information and to distinguish this definition from others that appear in the literature.

The formula for information shows that bits on the microscopic level are conceptually the same as bits on the macroscopic level. The formula allows us to determine the quantitative relationship between information and entropy, a topic which has led to much confusion in the literature.

The minimum energy that must be dissipated in order to gain one bit of information, ${\cal E}_{min}= k_{\mbox{\scriptsize B}}T \ln(2)$ joules per bit, is first derived from the Second Law of Thermodynamics. The derivation is straight forward, given the definition of information, but to my knowledge it does not appear in the literature.

The same formula for ${\cal E}_{min}$ is then derived from the machine capacity formula, equation (17).

I then show that molecular machines perform precise logical operations. This implies that computers made from single molecules are possible. Such computers should be able to approach the ideal minimum energy dissipation.