One detail of the Darwinian paradigm Miss Rand probably did not know is that its account of the origin of life itself — which account goes under the general name of abiogenesis or chemical evolution (i.e., the putative genesis of biological organisms from previously existing non-living, non-biological chemicals) — violates a fundamental law of physics; and not just any old law of physics, but THE great law of physics, as it is the law that actually determines the ice-cold fact that time flows in one direction only. This law is the Second Law of Thermodynamics, sometimes poetically called Time's Arrow but in most other occasions (at least, informally) referred to simply as entropy.
There are different ways of thinking about entropy, but they all involve the idea of "states of disorderliness" of a system. Disorderliness, not orderliness. As a system becomes more disorderly, its entropy is said to increase; conversely, as a system becomes more orderly, its entropy is said to decrease. If the metric one uses to measure disorderliness is a macroscopic one like "energy," then entropy can be thought of as the amount of energy in a system that is unavailable to perform work; if the metric one uses is a microscopic one like "the configuration or arrangement of particles comprising the system," then entropy can be thought of as the inevitable tendency for the particles comprising a system to move from some initial arrangement that is improbable toward an arrangement that is more probable. The microscopic and the macroscopic are related, of course, for as a configuration of particles moves from one of low probability to one of high probability, less energy is available in the system to perform work. The arrangement of particles that corresponds to the maximum amount of unavailable energy is one that has the least order, i.e., that arrangement which is the most random and the most probable. Thus, the Second Law of Thermodynamics dictates that Time's Arrow move any system of particles from states of orderliness to states of increasing randomness. In other words, the inevitable result of time on any system is to cause it to have more disorder and more random configurations amongst its constituent elements.
Taken by itself, this consideration of Time's Arrow always to move systems in the direction of dissolution might be enough to dismiss any claims of abiogenesis regarding a configuration of particles (i.e., prebiotic chemicals) presumably moving from an assumed initial state of randomness to a final state of orderliness, i.e., a living organism. But there's a catch that is skillfully exploited by the advocates of chemical evolution: the mathematics of the Second Law of Thermodynamics tell us that an increase in entropy is inevitable only in systems that have partitioned themselves off from the rest of existence in such a way that neither matter energy can enter or leave. Such a partitioned off system is known as a closed system. Thus, in a hypothetical perfectly insulating Thermos bottle initially filled with ice-cubes and hot tea, Time's Arrow dictates that the hot tea shall NOT draw energy from the ice-cubes in order to keep itself hot and keep the ice-cubes cold, but, rather that the ice shall warm and melt, and the tea shall cool a bit, until the entire initial ice-cube/hot-tea "system" reaches one uniform temperature. There is no longer any available energy inside this Thermos to perform work; all of the particles inside the Thermos have reached their most highly probable arrangement, and the system has reached "maximum entropy" or equilibrium.
This is quite different, however, from a situation in which matter and energy can pass freely to and from the Thermos container itself. The Thermos is now not partitioned off from the rest of existence, and is "open" to it; so such a system is called an open system. In such a system, both particles (e.g., more ice-cubes) and energy (e.g., a heat source) can enter the Thermos from some other place and constantly replenish the initial conditions; so long as ice-cubes and heat were entering the Thermos from outside, the entropy inside the Thermos could be maintained at a constant, or even be made to decrease (by having a colder, lower-entropy outside environment, thus drawing heat out of the Thermos and causing the hot-tea itself to freeze into a low-entropy, crystalline structure of ice). Thus, according to the advocates of chemical evolution, the Second Law of Thermodynamics remains inviolate in their various scenarios because the energy needed to "finance" the building up of orderliness from chemicals to living organisms is provided by stellar radiation, mainly from the sun. According to this view, the lowering of entropy in chemicals on Earth as they move from their initial high probability states as chemicals to their resultant low probability states as living organisms is compensated by the fact that the sun itself, which is financing the reduction in entropy on Earth, is moving toward a state of even higher entropy than it originally had at a faster rate. Thus, according to this view, the total entropy of the open Earth/sun system exactly obeys Time's Arrow, as it must, even if in a small part of that system — on Earth — the local entropy appears to have decreased with the emergence of life from non-life.
This is a very common view. So long as the system in question is open — permitting both matter and energy to pass through the system's barrier (i.e., the walls of the Thermos container, or the atmosphere of planet Earth) from some other place outside the original system —there is no violation of Time's Arrow, since energy can be imported from some other place to finance a local reversal of entropy.
Recently, however, a professor of mathematics at University of Texas named Granville Sewell took a second look at the Second Law of Thermodynamics and asked a simple, if profound, question: Can Anything Happen in an Open System? Given an open system between Thermos and Surrounding Freezer, does it follow that anything is as likely as anything else to occur inside the Thermos simply because ice has been made more likely? His answer may surprise you. And though the original papers are available online, you can watch two explanatory videos at the links below. The first is posted at University of Texas El Paso and narrated by Professor Sewell himself; the second is a simplified explanation of his position that was recently posted to YouTube. Though the first is quite a bit more challenging than the second, I recommend watching them both.