Is there a fourth law of thermodynamics, or some cousin of it, concerning self constructing non equilibrium systems such as biospheres anywhere in the cosmos?
I like to think there may be such a law.
Consider this, the number of possible proteins 200 amino acids long is 20 raised to the 200th power or about 10 raised to the 260th power. Now, the number of particles in the known universe is about 10 to the 80th power. Suppose, on a microsecond time scale the universe were doing nothing other than producing proteins length 200. It turns out that it would take vastly many repeats of the history of the universe to create all possible proteins length 200. This means that, for entities of complexity above atoms, such as modestly complex organic molecules, proteins, let alone species, automobiles and operas, the universe is on a unique trajectory (ignoring quantum mechanics for the moment). That is, the universe at modest levels of complexity and above is vastly non-ergodic.
Now conceive of the "adjacent possible", the set of entities that are one "step" away from what exists now. For chemical reaction systems, the adjacent possible from a set of compounds already existing (called the "actual" ) is just the set of novel compounds that can be produced by single chemical reactions among the initial "actual" set. Now, the biosphere has expanded into its molecular adjacent possible since 4.8 billion years ago.
Before life, there were perhaps a few hundred organic molecule species on the earth. Now there are perhaps a trillion or more. We have no law governing this expansion into the adjacent possible in this non-ergodic process. My hoped for law is that biospheres everywhere in the universe expand in such a way that they do so as fast as is possible while maintaining the rough diversity of what already exists. Otherwise stated, the diversity of things that can happen next increases on average as fast as it can.