Entropy, when taken as a measure of the disorder or randomness in a closed thermodynamic system, has obvious similarities to impermanence. Granted, they are not the same thing and much of what is considered entropy and much of what is considered impermanence cover separate topics, but the overlap in the Venn Diagram of the two is considerable. Among other differences, entropy might be considered to apply to closed systems, while impermanence is usually thought of as applying to individuals or individual objects in that system.
Regardless, living beings are every bit as subject to entropy as are gas molecules in a room, the classic example of entropy. It takes effort for a living being to not succumb to entropy and not have its body dissociate and disperse across the biosphere, but that is exactly what happens in death and decay. Every living body eventually succumbs to entropy, and the highly organized bodies and organs that contained and sustained its life do not stay that way forever. To say that everything is impermanent is to say that everything ultimately succumbs to entropy. A physicist might say that life-and-death is a sequence from a low to a high state of entropy.
Have you ever seen one of those time-lapse movies of an animal decaying, like during the title sequence of the HBO show True Blood? That's entropy - the body itself becoming disorganized and literally falling apart, and then those parts entering the food chain and dispersing across the globe, or becoming part of the soil, or being taken up by plant life and entering the food chain in that manner. The inability to keep a body intact and highly organized forever is also known as impermanence.
All living beings, in order to survive, work to maintain a state of low entropy and to avoid states of high entropy. But reduction of entropy in an individual results in an increase in entropy outside of the individual. As described by Ling Chen of the University of Northern British Columbia, "Living organisms need to extract low entropy from the environment, to defend their low entropy sources, and to reduce the diffusion of the low entropy. The struggle to stay in low entropy states is called natural selection." It's even more obvious when stated that natural selection is the struggle to avoid impermanence.
Displays of low entropy levels evolved as a signal of attractiveness in the process of natural selection, and organisms can advertise their suitability as potential mates by appearing to avoid impermanence. According to Chen,
"As both natural selection and sexual selection favor low entropy state, the pursuit of low entropy becomes the main motive of human mind and animal mind. Indeed, the low entropy state is the main way of advertisement for most sexually reproducing species. Large body size, colorful and highly complex feather patterns with large amount of information content, and exotic structures are all different representations of low entropy states."
Among us humans, displays of apparent permanence are accomplished through the accumulation of wealth, conspicuous consumption, demonstrations of athletic prowess, and creation of works of art, all of which represent different forms of low entropy. People signal their low-entropy state by buying ever-more expensive houses, cars and clothes, going to more expensive restaurants, and attending more exclusive schools. The great efforts human beings put into these activities reflect the importance of hiding the appearance of impermanence.
So much of human suffering revolves around the inevitability of impermanence and the effects entropy has on us. However, it appears that clinging to low states of entropy is something that is hard-wired into our DNA. The Indian sage Nagarjuna said that the mind that sees the impermanence of the world is the mind of wisdom. I wonder if Max Planck ever thought that wisdom was the recognition of entropy.