Synergy and matter behavior, a new approach

. Until now synergistic effect is considered only the case when the final effect of the simultaneous action of several loads is greater than the sum of the partial effects. But the sum refers only to linear behavior of matters. In the general case of nonlinear matter behavior the paper shows that the synergistic effect may be positive (the total effect is greater the sum of the individual effects), negative (the total effect is less the sum of the individual effects) or zero (the total effect is equal the sum of the individual effects). The synergistic effect depends on the matter behavior. Some general examples and practical examples allowed a generalization of the problem of synergistic effect.


Introduction
The concept of synergy comes from the Greek word synergos which means "to work / act together", to achieve a certain goal/effect. In general, synergy means the association or cooperation of several factors to produce a certain effect, which cannot be achieved through the individual actions of the factors involved. Synergy is related to an interdisciplinary field. At present, synergy often means the simultaneous action, in the same sense, of several loads, with a final effect that is greater than the sum of the partial effects corresponding to each load. The evaluation of the synergistic effects was done at the macroscopic level [1; 2], as well as at the cellular or molecular level [3]. Molecular evaluation is particularly important in analyzing the influence of any actions on living organisms, like drugs *Correspondence address: vvjinescu@yahoo.com synergism quantification, nutrients and pharmaceuticals combination [4]. Any traditional systems of medicine may have a synergistic approach [5]. These all cases corresponds to the traditional definition of synergistic effects (the effect of the whole is greater than the sum of the effects of the individual parts). The International Journal of Synergy Research in Life Science, for example, is dedicated to application of synergy concept at the molecular, cellular and organisms levels, in the prevention and treatment disease. However, only sometimes is the final effect greater than the sum of individual effects. There are times when the final effect is equal to, or even less than, the sum of individual effects. This is why it is easier to say synergy than to prove [6]. The following argumentation mathematically shows that the synergistic effect may be positive, zero or negative. This depends on the behavior of the matter in relation to the load to which it is subjected.

The influence of matter behavior on synergistic effect
• In the case of linear behavior, a load Y on a physical body determines an effect X, between which the correlation is linear, of the form, (1) where B is a constant of the material under load. For example, when bending a bar, placed on two supports (Fig. 1), the following are obtained [7], arrow x1 under force F1; -arrow x2 under force F2; -arrow x1,2under the sum force. In the case of the linear-elastic behavior of the bar (1), that is, the effect of the action of the total force is equal to the sum of the individual effects. The synergistic effect is zero. Relation (2) expresses the classical principle of superposing effects according to which "the total effect (X) is equal to the sum of individual effects (Xi)", This relation is valid only if: -the Xi effects are measured with the same unit of measurement; -the dependence between the load and the effect is linear (1). With a few exceptions, most of the laws of behavior currently used in various chapters of science are linear [8]. For example: Hooke's law, Newton's laws, Ohm's law, Fourier's law, Fick's law, the law of magnetic induction, etc.
In the case of nonlinear behavior, depending on power, the law is used [8; 9], where Y has the meaning of a generalized load, which may be at macroscopic or microscopic level, as well as at molecular or cellular level. C and k are material constants. Using relation (3) in the case of nonlinear behavior leads to incorrect results. If two loads of the same nature and type, 1 Y and 2 Y act on a nonlinear physical body (4) and produce the main effects 1 X and 2 X , then If the total load ( ) produces the total effect X, one may write From the comparison of the last relations it results, which shows that in the case of nonlinear behavior, that is, the total effect is different from the sum of partial effects. One defines: the positive synergistic effect if the total effect is greater than the sum of individual effects; the negative synergistic effect, if the total effect is less than the sum of individual effects; the zero synergistic effect, if the total effect is equal to the sum of individual effects.
If the effect of two or more actions on a body is stronger / greater than the sum of the individual effects determined by each action, it means that the total effect X fulfills the condition, where Such a correlation defines positive synergy and it is obtained if the exponent from the law of behavior (4) 1  k . For example, with If the matter behaves nonlinearly and is characterized by , which is greater than If the total effect of several simultaneous loads is less than the sum of the individual effects, then where , which is less than the sum 11 2 1 = + X X .
In conclusion, for: 1  k one obtains a positive synergistic effect; the total effect is greater than the sum of partial effects; 1 = k , zero synergistic effect, the total effect is equal to the sum of partial effects; 1  k , one obtains a negative synergistic effect, because the total effect is less than the sum of partial effects. It follows that the synergistic effect is a consequence of the value of the exponent in the law of matter behavior. The influence of matter behavior upon the synergistic effect may be easy understand from the graphics of matter behavior in the figure 2. In case exponent 1  k (Fig. 2, a), under the same stress Y1, the effect 2 X  for the material whose exponent Under the same load Y1, the effect is different depending on exponent k in the law of behavior, namely: Fig. 2, a); Fig. 2, b). Under the action of several loads Yi , one may write that,

Practical examples
Some examples [10]: when the effects of sulfur dioxide superposes with particles in suspension, such as for instance ash dust, a positive synergistic effect is obtained. The combination of these pollutants may increase mortality from cardiorespiratory disorders and deficiencies of lung function; short-term exposure to nitrogen oxides (especially NO and NO2) leads to changes in respiratory function (emphysema, increased susceptibility to bacteriological infections of the lungs), but if they are mixed with ozone, as well as in the presence of suspended dust, nitrogen oxides have positive synergistic effects.
• In Rheology and in Fluid Mechanics one comes across fluids that are: -Newtonian, whose behavior is defined by Newton's law, where τ is the shear stress; is the shear rate (γshear strain; t -time); 0 μ -shear viscosity, constant; -non-Newtonian, whose behavior is given, by example, by the Ostwald-de Waele law, wherein τ K and ν are fluid constants. One can also find synergistic effects when fluids flow. Fluid rheograms show dependence γ τ  − (Fig. 3), which resembles Figure 2. Fluid with 1   are called pseudoplastic (Fig. 3, a), and those with 1   are called dilatant (Fig. 3, b) [11]. One notices that: Here 1 γ  is the shear rate corresponding to the linear relationship (12) between τ and γ  .
Consequently, taking into account a load with shear stress τ, it may be generally written In the case of linear behavior, (12), • In the case of chemical reactions, the synergistic effects separate exothermic reactions from endothermic reactions. For example, consider a reaction between two substances A and B, from which two other substances C and D are obtained. During the chemical reaction a certain amount of energy is released or absorbed. You can write, The amount of energy E  : -is released during the chemical reaction as a result of the transition from the energy level E1of system ( ) and the total internal energy of the reaction products, where i can be equal to j or, differently from it, the general relation can be written, wherein A and kE are system constants consisting of reactants and reaction products.
the reaction is exoergonic, or exothermic and corresponds to the positive synergistic effect.
In figure 4, b the reaction is endoergonic, or endothermic and corresponds to the negative synergistic effect. Here

Generalization
One writes YT for the total simultaneous action on a physical body and XT for the total effect obtained. In the spirit of synergy the following general relation can be written

Conclusions
Synergy is related to the interdisciplinary field. Nowadays synergistic effect is only the case when the effect of the whole is greater than the sum of the effects of the individual parts. Taking into consideration the nonlinear, power law, behavior of matter, the paper shows three kinds of synergistic effects, namely positive, negative and zero. The general and practical examples of synergy analyzed allowed a useful generalization of the problem of synergistic effect.