In the End Heat Death Entropy and the Arrow of Time

Can thermodynamics provide us with the desired proof of an irreversible direction of time? To answer this question, I will turn directly to the Second Law of Thermodynamics, which was first formulated by Rudolf Clausius during the second half of the nineteenth century and now exists in various formulations. For the purposes of this study, I will use the following wording: In an isolated system, entropy never decreases; in the case of reversible processes, it remains constant; and, in the case of irreversible processes, it continually increases.

While an open system can exchange energy and matter with its environment, a closed system exchanges only energy with its environment. A theoretical idealization of the closed system that is often used successfully is the isolated system, in which neither matter nor energy is exchanged. Entropy denotes the measure of disorder in a system. In everyday life, we experience entropy in many ways: Hot coffee cools off at room temperature; it has not yet been observed that milk poured into coffee spontaneously separates out again after dispersing, although according to the laws of classical mechanics, this must be possible. These observations create enigmas. How can it be that coffee and milk follow a temporal sense of direction although the laws that determine the behavior of coffee and milk molecules are time-symmet-ric?283

But it is not only the domestic coffee table that obeys the Second Law; even our solar system continually complies with it. The sun is slowly burning its nuclear energy; it will radiate light and warmth until its collapse in approximately five billion years, and thus, with every photon emitted, it increases entropy in the universe. Applied to the universe as a whole, the theorem of ever-increasing entropy therefore means that the order in the universe is moving toward decay. In this context, one frequently speaks of the inevitable heat death of the universe. This does not mean that the universe is being destroyed by heat. Nor does it mean directly that the heat is disappearing and extreme cold will rule. What is "dying" is the exchange of energy, so that ultimately there will no longer be a gradient between different levels of energy. Heat death thus signifies complete heat equalization (thermal equilibrium) and maximum disorder. A state has been reached where time has ceased to flow. This is why thermal balance is also called a "time peak" \Zeit-gipfe[\2U At the time peak, an isolated system is cut off from a possible future because it can no longer change. It also no longer has access to its past, for the development cannot be directed backwards by the decrease in entropy. For the first time, something like a historical dimension becomes visible in physics itself.285 The irreversibility in thermodynamics invites one to rethink the relationship of being and becoming. For Newton it was reasonable to understand the universe as a pattern of eternally existing elements. Thermodynamics, on the contrary, urges one to understand becoming as the basic structure of the universe.

Because of the insights in thermodynamics, a modification of the concept of the universe was called for. The view of the universe as a perfect machine as found in Newtonian physics is no longer tenable. The conception of a uniform and, in principle, infinite universe was replaced by the concept of the universe as a heat engine that ultimately destroys itself: no longer an eternal machine, but, rather, a programmed apocalypse.

Here, one may feel compelled to object. How can the Second Law claim absolute validity when, at the same time, we can so often observe an increase in order and a development of higher complexity? Is there not an irreconcilable conflict between thermodynamics and the principle of evolution?

There are several possible answers to this question: First, when order increases at a certain place in a system, we are dealing with a local decrease in entropy that has no effect on the increase in entropy in a system as a whole. Second, under certain conditions, Poincare's Theorem allows the notion of reverse entropy—i.e., increase in order—for, according to Henri Poincare, every isolated system eventually returns to its initial state; it is cyclical. The period of such a cycle is unimaginably long, to be sure, but finite. Thus, on the condition of a sufficiently long period of time, a "resurrection" from cosmic heat death is theoretically possible. A third answer has been formulated by the "Brussels School," led by Ilya Prigogine.286 They have shown that, far from equilibrium, so-called dissipative structures287 make developmental leaps.

This can be understood as follows: Systems that are not in thermodynamic equilibrium develop toward a final state in which all change ceases. This targeted end-point is called an "attractor." For systems that are located near equilibrium, this development is linear, i.e., with direct proportionality of forces and effects. For systems that are far from thermodynamic equilibrium, this development is nonlinear and precisely these systems can be used to explain the apparently impossible increase in order. The overwhelming majority of everyday life processes consists of such open systems that exchange energy and matter with other systems and that are located far from equilibrium. If these systems are sufficiently far from the state of equilibrium, they can branch out at a critical so-called bifurcation point. Their development becomes unstable, and they "leap" into another state that can be quite well ordered and display new shapes and properties. In this way, diverse patterns with a large number of bifurcation points can be created. These complex processes, which can interact and lead to complicated structures, are called self-organization or autopoiesis.288 Such developmental leaps to a higher order occur without violating the Second Law of Thermodynamics.

Viewed as an open system far from equilibrium, the universe is therefore not on a straight path to heat death. It is instead encountering bifurcation points continually on its path and thus also the possibility of spontaneous self-organization of galaxies as well as cells. Because these processes are irreversible, time appears to have a direction. It remains a question of interpretation whether this means that the development of entropy and the time arrow can be regarded as identical.289 Nevertheless, it seems that the key to understanding the time arrow lies in the stability properties of complex systems. Within the framework of chaos research, remarkable results have been achieved in this regard.

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