## Case 3 Information and Entropy

The following short passage from Julius Caesar, Act IV, Scene 3, is spoken by Brutus, when he realizes that he must face Mark Antony's army. It is an information-rich nonrandom arrangement of 125 letters of the English alphabet:

certain amount of work. The amount of energy available to do work is the free-energy change, AG; this is always somewhat less than the theoretical amount of energy released, because some energy is dissipated as the heat of friction. The greater the elevation of the larger object, the greater the energy released (AG) as the object slides downward and the greater the amount of work that can be accomplished.

How does this apply in chemical reactions? In closed systems, chemical reactions proceed spontaneously until equilibrium is reached. When a system is at equilibrium, the rate of product formation exactly equals the rate at which product is converted to reactant. Thus there is no net change in the concentration of reactants and products; a steady state is achieved. The energy change as the system moves from its initial state to equilibrium, with no changes in temperature or pressure, is given by the free-energy change, AG. The magnitude of AG depends on the particular chemical reaction and on how far from equilibrium the system is initially. Each compound involved in a chemical reaction contains a certain amount of potential energy, related to the kind and number of its bonds. In reactions that occur spontaneously, the products have less free energy than the re-

(a) Mechanical example

There is a tide in the affairs of men, Which, taken at the flood, leads on to fortune; Omitted, all the voyage of their life Is bound in shallows and in miseries.

In addition to what this passage says overtly, it has many hidden meanings. It not only reflects a complex sequence of events in the play, it also echoes the play's ideas on conflict, ambition, and the demands of leadership. Permeated with Shakespeare's understanding of human nature, it is very rich in information.

However, if the 125 letters making up this quotation were allowed to fall into a completely random, chaotic pattern, as shown in the following box, they would have no meaning whatsoever.

In this form the 125 letters contain little or no information, but they are very rich in entropy. Such considerations have led to the conclusion that information is a form of energy; information has been called "negative entropy." In fact, the branch of mathematics called information theory, which is basic to the programming logic of computers, is closely related to thermodynamic theory. Living organisms are highly ordered, nonran-dom structures, immensely rich in information and thus entropy-poor.

(a) Mechanical example aG < 0

Loss of potential energy of position

I Endergonic

Exergonic aG < 0

Loss of potential energy of position

I Endergonic

(b) Chemical example

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