326 George A. Sacher 



The information function is thereby resolved into separate terms for the expected 

 values and for the deviations from expectation. The analysis of fluctuation 

 processes falls into the latter class. 



The formal equivalences between fluctuation entropy and Fisher information 

 does not imply complete equivalence of the concepts. The theory of entropy 

 fluctuations deals with the stationary fluctuation process in a single individual 

 or in a group of indistinguishable individuals, where in either case the ergodicity 

 condition is satisfied. There is no such restriction on the applicability of the 

 Fisher information. The case of non-ergodic populations (individual differences 

 in parameters) can be covered by obvious generalizations of the fluctuation 

 theory, so this distinction is not a permanent one. 



Determination of the Lethal Bound 



Thus far in the presentation the existence of the lethal boundary surface has 

 been a postulated property of physiologic mechanisms. In terms of the linear 

 models of fluctuation processes that have been discussed the lethal bound is 

 of necessity an arbitrarily assumed property, for a continuous linear process 

 by its nature has no failure point. The escape from this unsatisfactory situation 

 is by way of a more thorough mathematical analysis of homeostatic properties. 

 The lethal boundary has a natural interpretation as a 'divide' on a potential 

 surface (compare with Fig. 2). When it is possible to discuss the homeostatic 

 processes as non-linear systems with multiple equilibria, the lethal bound, and 

 also the boundaries between different viable steady states, will appear as 

 necessary topological properties of the physiologic mechanisms. We have under 

 way some investigations of simple non-linear stochastic mortality models, and 

 the early results are quite interesting (6). 



VII. ENTROPIC CONTRIBUTION TO THE AGING PROCESS 



Brief consideration was given above to the direction of change of homeo- 

 static parameters with age. This section will deal with the influence of physiologic 

 fluctuation on the rate of aging. 



It is an intuitive judgment that physiologic steady states of organisms tend 

 to maximize the efficiency of physiologic function in the environments to which 

 the organisms are fitted. The approach to greatest efficiency is presumably by 

 means of natural selection operating on the genetically controllable thermo- 

 dynamic properties of enzymes. The characteristics of physiologic performance, 

 and in particular the values of the phenomenological rate constants are ultimately 

 dependent on the activities, specificities and stabilities of the constituent 

 enzymes. Thus, to give an account of the age changes in the values of the 

 phenomenological parameters one must turn to the consideration of function 

 at the biochemical level. The rate at which irreversible change occurs in a 

 biological system will be discussed for three situations: 



(a) as a function of temperature, independent of metabolic activity; 



(b) as a function of metabolic activity in an undisturbed steady-state; 



(c) in a steady-state disturbed by ffuctuations much greater than thermal, 

 i.e. by the fluctuations of physiologic state discussed above. 



The analysis of irreversible molecular changes as a function of temperature 



