78 TEMPORAL ORGANIZATION IN CELLS 



This quantity may be positive or negative, and we adopt the convention in this 

 context that if the quantity i/jq—^i is positive, then talandic work is done by 

 the epigenetic system since then its final free energy value, ipi, is smaller than 

 its initial value, iJjq. But ifi/jQ—ipi is negative, then we will say that talandic work 

 is done on the epigenetic system by some stimulus. Regarding s^ as an inductive 

 stimulus, for example, the quantity i/^Q—i/'i represents the amount of talandic 

 work which must be done by the stimulus when it acts very slowly (reversibly) 

 and with 6 held constant. However, in a real inductive process which occurs 

 irreversibly and with 6 also changing, the amount of talandic work which 

 must be done by the stimulus to cause such a change of state in the epigenetic 

 system will be greater than this. 



We now have a complete set of functions with which to study the "thermo- 

 dynamic" properties of oscillating control systems of the type considered in 

 this work. It would be premature to develop the mathematical properties of 

 these functions further before some experimental justification is found for 

 their utility in the analysis of cellular activities. The first step is, of course, 

 to establish the existence of the parameter 6 for resting cells, and to demonstrate 

 that different G-states occur in analogy with energy states in physical systems. 

 An experimental approach to this question is suggested in Chapter 8. Only 

 after such an investigation will there be any reason to study further the pro- 

 perties of the thermodynamic functions associated with talandic phenomena 

 in cells. 



There is one feature of the present theory which, in comparison with 

 classical thermodynamics, is conspicuous by its absence. No evidence of 

 anything analogous to a potential function has arisen in this study. In classical 

 theory the energy of a physical system is made up of two parts, one kinetic and 

 the other potential. In simple conservative systems the variables also divide 

 in the total energy function or Hamiltonian, momenta entering into the 

 expression for the kinetic energy, while the variables of position define the 

 potential energy. Although we have a complementarity of variables in our 

 theory, which is formally analogous to that in physical systems relative to 

 position and momentum coordinates, the analogy does not extend to the exis- 

 tence of two different types of G, "kinetic" and "potential". Whereas in 

 physics we can have /?,• (momentum) = constant without having c, (posi- 

 tion) = constant, in the epigenetic system if .y, = constant then it is necessarily 

 zero (i.e. Xi = Pi, the steady state value), and this has the immediate con- 

 sequence that yi = also (i.e. Y, = q^, hence ^ = and the system is in its 

 ground state. Both epigenetic variables are thus analogous to momenta and 

 all "energy" is "kinetic". 



It is possible that a potential function may be found for systems of coupled 

 non-linear oscillators, however, in relation to the distribution of oscillator 

 frequencies relative to one another. The fundamental distinction between 

 linear and non-linear oscillators is that the former show additive, non- 

 interacting behaviour, whereas the latter always exhibit an interaction of 

 some kind. As Minorsky (1962) has observed: "Perhaps the whole theory 

 of non-linear oscillations could be formed on the basis of interactions." 



