No actually this is one perpetuating myth about entropy that even scientists themselves (and school curricula) propagate.
To answer this and dispel the myth, ask this simple question: disorder with respect to what exactly?
Why is a uniform gas disordered than a gas with two phases?
Of course a uniform gas has more (another) symmetry, in fact aquires the symmetries of the underlying environment. But so does the the two-phase gas, it has a certain symmetry (and not others) deriving from the underlying environmental process. So far so good. Where is the "disorder" exactly, and with respect to what and to whom is this a "disorder"? i think you get the point meant here.
Clearly there is a very subjective (to mention the least) concept of disorder used here which is not explained anywhere. Just stated as fact which is not.
Some take this further equating entropy with death vs life which is even more absurd. One can have a series of cages perfectly ordered, yet one will not have life in them.
Please consider this before you just accept anything thrown at you sounding scientific (while it is not)
If you want the full scientific version of this answer check (especialy) the works of I. Prigogine on Entropy, Complex Dynamic Systems and Biological Systems. e.g "From Being to Becoming: Time and Complexity in the Physical Sciences"
Other schools of thermodynamics also have similar approaches and hard facts to consider. For a popular, yet somewhat thorough exposition check, for example: "The Arrow Of Time: A Voyage Through Science To Solve Time's Greatest Mystery"
- is NOT disorder (mechanistic approach)
- is NOT lack of information (bayesian/subjectivist approach),
- is NOT contrary to evolution (inteligent design-approach)
- is NOT simply a statistical effect (quantum-mechanical/statistical approach)
- is NOT related solely to linear and (static) equilibrium processes, in fact entropy and (yes) the 2nd Law have been generalised (i would say simply clarified) for (dynamic) non-equilibrium / non-linear processes
Refer to "What is the second law of thermodynamics and are there any limits to
In the scientific and engineering literature, the second law of
thermodynamics is expressed in terms of the behavior of entropy in
reversible and irreversible processes. According to the prevailing
statistical mechanics interpretation the entropy is viewed as a
nonphysical statistical attribute, a measure of either disorder in a
system, or lack of information about the system, or erasure of
information collected about the system, and a plethora of analytic
expressions are proposed for the various measures. In this paper, we
present two expositions of thermodynamics (both ’revolutionary’ in the
sense of Thomas Kuhn with respect to conventional statistical
mechanics and traditional expositions of thermodynamics) that apply
to all systems (both macroscopic and microscopic, including single
particle or single spin systems), and to all states (thermodynamic or
stable equilibrium, nonequilibrium, and other states). .. Here entropy
emerges as a microscopic nonstatistical property of matter.
Entropy is one of the most basic facts (and least understood, analysed) related directly to causality, the arrow of time, quantum-mechanics and evolution.
In fact most (if not all) time-reversible equations are wrong (ot at least crude approximations) rather than entropy and the time arrow itself.
To quote the cosmologist Arthur Eddington:
The law that entropy always increases holds, I think, the supreme
position among the laws of Nature. If someone points out to you that
your pet theory of the universe is in disagreement with Maxwell's
equations - then so much the worse for Maxwell's equations. If it is
found to be contradicted by observation - well, these experimentalists
do bungle things sometimes. But if your theory is found to be against
the Second Law of Thermodynamics I can give you no hope; there is
nothing for it but to collapse in deepest humiliation.
The references given above dispel all these misconceptions.