Entropy decrease?

Robert M.Wald in The Arrow of Time and the Initial Conditions of the Universe (Enrico Fermi Institute and Department of Physics University of Chicago, arXiv:gr-qc/050709 vl 21 Jul 2005) writes:

“There is no question that our present universe displays a thermodynamic arrow of time: We all have observed phenomena in our everyday lives where entropy is seen to increase significantly, but no one has ever reliably reported an observation of entropy decrease in a macroscopic system.”

We can have a different approach. After the Big Bang all visible matter undergoes temperature decrease and its entropy is changing due to dS=dQ/T=mcdT/T, where m - mass, c - the heat capacity. After integrating we get the entropy change  ΔS=mc lnT/T0, where T0 – the temperature at which all molecules of matter have zero kinetic energy.

Besides we have step-by-step entropy decreases due to phase changes: radiation – atoms – molecules – gas – liquid – solid.

Some say that after the heat deaf the entropy of the Universe is maximal. It depends on approach, depends on POV, or on distribution we look at. At heat deaf the atoms and molecules are maintained, so is the information originated at their formation. Robert Ayres in his book “Information, Entropy and Progress”  names it the ‘morphological information’.

The Second Law was formulated by observations on Earth: by all physical processes where labor or heat is exchanged entropy increases. For example, Earth radiates the heat dQ into the environment. Earth’s entropy change dS=–dQ/300 (when heat is received, it is designated by +dQ, when heat is given away, it is designated by –dQ), environment receives the radiated heat, its entropy changes dS= +dQ/2,7. The system’s ‘Earth-environment’ total entropy changes dS =dQ/2,7–dQ/300 is positive.

What is ‘the environment’? Vacuum + photons (I don’t discuss dark matter). On a cosmic scale all the photons emitted by stars get redshifted due to expansion of the Universe. Does their entropy get decreased too?

It seems that we are not forced always to say that there is a global increase of entropy due to the Second Law. It seems that we can reliably report “an observation of entropy decrease in a macroscopic system.”