Entropy

            Entropy is a measure of chaos. The second law of thermodynamics suggests that our entire universe is slowing down, because its entropy, or its need for sustaining energy, is increasing. One of the results of this law is the prediction there that can be no perpetual motion machine (the first law tells us no perpetual motion machines exist of the “first kind;” the second law of the “second kind”). All systems wear down; energy is lost and cannot be totally recovered by a system. We can also consider entropy to be a measure of internal randomness, or molecular chaos. As entropy increases, chaos increases. 

            Arthur Eddington called entropy, time's arrow and this name has been adopted by modern science (Angrist & Hepler, 1967). Entropy is an important concept in thermodynamics. The second law of thermodynamics defines entropy as a measure of needed energy. Entropy is a measure of a system's disorder. Entropy is also a measure of molecular randomness. Thus a solid has less entropy than a liquid, which has less than a gas (Angrist & Hepler, 1967).

            The inequality of Clausius, a corollary of the second law, states that any change in energy with respect to temperature must be less than, or equal to, zero. In other words, the energy of any periodic system naturally tends to decrease. Mathematically we can say that:

so that entropy, S, over an entire cycle of a system, can be defined for a reversible process as:

            Here S is called the Clausius's Entropy after Rudolph Clausius, who first conceived the idea of entropy.

            For closed systems (systems that function independent of their environment) it can be demonstrated that:

            This equation expresses the principle of the increase of entropy. All processes in closed or isolated systems have increasing entropy. This is another way of saying that only those processes can naturally take place where entropy will increase. This is a law of closed-system thermodynamics. This law applies to all physical engines including our bodies and to all systems including our world when they are considered closed or isolated from their environments. 

            The general equation for an open system is:

            As a tiny mass dm_i enters into the system, the entropy is increased by the amount dm_is_i. As the mass dm_o leaves the system, the entropy is decreased by the amount dm_os_o. In addition mass, energy, and information can also be exchanged across the boundary of an open system. Until recently, one spoke of systems as being either closed to their environments, or open to them. Today, thermodynamics recognizes three types of systems: (1) isolated, which do not share matter or energy with their environments, (2) closed, which share energy and/or information but not matter, and (3) open, which share matter and energy and/or information. (Kondepudi & Prigogine, 1998)

            There are several other entropies today in addition to that of Clausius. Prigogine's Entropy, for example, addresses what is called far-from equilibrium thermodynamics which looks at nonlinear dynamic processes and self-organizing systems such as the cells of our body. The equation for Prigogine's Entropy is:

where dS_T is the total entropy change, dS_I is the change in internal, or Clausius' Entropy, the entropy produced by irreversible internal processes, and dS_E is the entropy exchanged with the surroundings (this term is zero for isolated systems for which Prigogine’s Entropy is identical to Clausius’ Entropy). While dS_I tends to increase, the term dS_E can increase or decrease or remain zero (it is positive if entropy enters the system and negative if entropy leaves the system). The important effect of Prigogine's Entropy is that the total system, entropy change of any open system, dS_T, can be positive, negative, or zero. Systems for which

dS_T < 0 (i.e., where entropy is decreasing) are said to be self-organizing (Çambel, 1993).

            Prigogine's Entropy implies that as systems become more complex, a threshold of complexity will be reached such that the system will begin functioning in unpredictable directions; such a system will lose its initial conditions and these can never be reversed or recovered (Briggs & Peat, 1989). For open systems, where dS_E is sufficiently negative that it exceeds the magnitude of dS_I,  then entropy will decrease (order will increase) over time during the process. This could help explain the thermodynamics of dissipative systems (those that required energy from external sources) and self-organizing systems (such as all living systems) (Kondepudi & Prigogine, 1998; Nicolis & Prigogine, 1989).

            Jacobi (1973) discusses entropy as:

Systems accessible to our experience are only relatively self-contained, we nowhere observe absolute psychological entropy, which could occur only in a perfectly self-contained system. But the more the partial psychic systems are closed off from one another and the more extreme the tensions between the poles, the more likely becomes the phenomenon of entropy (cf. The stiff, catatonic posture of many insane persons, their lack of contact with the world, their apathy, and seeming lack of ego, etc.). We often see this law, in a relative form, at work in the psyche....The irreversibility that characterizes energetic processes in inanimate nature can be modified only by artificial intervention (e.g., by technical or mechanical means). In the psychic system it is consciousness that can intervene to bring about a reversal. (pp. 56-57)

                        Both Jung and Jacobi necessarily addressed the entropy of Clausius which only holds for closed (i.e., isolated) systems (Prigogine’s Entropy for open systems was not widely accepted until the 1980s). However, as Jacobi rightly notes, the psyche is never totally closed to its environment. Although matter does not cross into or out of the psychic boundary, both energy and information do.   Today, we would apply Prigogine’s Entropy to the psyche as a self-regulating open system. The terminology here may be confusing.  The psyche is open to both energy and information, but not to matter (which is but a form of energy according to Einstein). In modern terminology, it would thus be called a closed system, but we will denote it as open throughout the remainder of this book to avoid confusion. The entropy of the psyche can be effectively increased (leading to an equilibrium state such as the emptiness of ego described by Jacobi above) or decreased (leading to normal healthy functioning) through the interfaces with both its external and internal environments.

            If we think of complex systems as being composed of millions of tiny subsystems (for example, the cells in our body, the citizens of a country, or the molecules in an object) then we will discover that each subsystem can act randomly while the overall system itself is in equilibrium and is relatively predictable. The theory of statistical mechanics, invented at the end of the last century, is one way of dealing with such subsystems. In this view, the system itself functions on the averages or probabalistic actions of its subsystems. For example, this is true for dissipative structures that are also autopoietic or self-organizing structures, which is to say, for living systems. Living systems maintain their dissipative structure by dissipating entropy before it has a chance to build up. Statistical entropy was created by the Austrian physicist, Ludwig Boltzmann. His equation is usually given as

 where S is the entropy, p_i is the probability of accessible states, and k is the Boltzmann Constant. 

            The higher the p_i, the higher the entropy (Çambel, 1993). Boltzmann’s Entropy indicates that entropy will always tend towards a state of maximum probability (Lebowitz, 1993). In order to apply this equation, all of the accessible states must have the same probability of occurring (Fast, 1962).

            When we view entropy as a measure of chaos, we can say that the probability of accessible states for any complex system is a measure of that system’s uncertainty. Ludwig Boltzmann was the first to note that entropy is a measure of molecular disorder and he concluded that increasing entropy implied increasing disorder (Prigogine, 1980). Irreversible thermodynamics deals with systems that change over time, but until recently it addressed only systems that are near to equilibrium conditions (Angrist & Hepler, 1967; Prigogine, 1997; Kondepudi & Prigogine, 1998).

            Jung wrote prior to the discovery of Prigogine’s Entropy. Thus, he was persuaded to regard the psyche as a “relatively closed system” in order to address the concept of entropy: He wrote: 

According to Boltzmann’s formulation, this leveling process corresponds to a transition from an improbable to a probable state, whereby the possibility of further change is increasingly limited. Psychologically, we can see this process at work in the development of a lasting and relatively unchanging attitude.  (Jung, 1981, p. 26)

            For Jung (1976), the psyche is governed by two important principles, entropy and the principle of equivalence. According to the principle of equivalence, any energy that disappears in one area of the psyche must appear in another area.

            Jung (1976) called the energy of the psyche the libido and described it as coursing through the psyche rendering its contents either conscious or unconscious. He writes, “We can say, then, that the concept of libido in psychology has functionally the same significance as the concept of energy in physics” (p. 131).

            The principle of equivalence is similar to the law of the conservation of energy found in physics. The total amount of libido remains constant but pockets of it can ebb and flow at various places throughout the psyche. Jung viewed the psyche as an arena where polar opposites are continually being balanced. Forces at the higher end of the psyche, the spiritual side containing the archetypes, are balanced by forces at the lower end of the psyche, the material side containing the instincts:

The psyche is made up of processes whose energy springs from the equilibration of all kinds of opposites. The spirit/instinct antithesis is only one of the commonest formulations, but it has the advantage of reducing the greatest number of the most important and most complex psychic processes to a common denominator. So regarded, psychic processes seem to be balances of energy flowing between spirit and instinct. (Jung, 1981, p. 207)

            When the psyche is considered as an open complex system, the law of energy conservation no longer applies. The psyche, like the physical body is dissipative, not conservative. Although Jung realized that the psyche is a complex dynamic system, it is now seen to be a great deal more complex than he believed. For example, while the libido is conserved, entropy can increase or decrease as the psyche interacts with its inner and outer environments--a fact unknown to Jung.