1.a In paragraph at Wikipedia/Entropy it is stated:
This is because energy supplied at a high temperature (i.e. with low entropy) tends to be more useful than the same amount of energy available at room temperature
1.b But at What is Entropy? there is:
The higher the temperature of the gas, the faster the gas particles are moving on average, so the wider the range of possible velocities for the gas particles, and hence, the more uncertainty we have about the velocity of any particular particle. Thus, higher temperature, as well as greater volume, mean higher entropy.
2.a I was trying to obtain information on relation between entropy and work. Basically, if an external process modifies a system so that its entropy is reduced, then it is expected by me that work was done on the system and energy was contributed to it. I received good answers ( Connection between entropy and energy ). However I feel that I was not properly understood.
2.b In 1953 paper of L. Brillouin ("The Negentropy Principle of Information") wrote what I basically had in mind when I asked the question. I am not aware if the approach is correct and accepted.
An isolated system contains negentropy if it reveals a possibility for doing mechanical or electrical work. If the system is not at a uniform temperature T, but consists of different parts at different temperatures, it contains a certain amount of negentropy. This negentropy can be used to obtain some mechanical work done by the system, or it can be simply dissipated and lost by thermal conduction. A difference in pressure between different parts of the system is another case of negentropy. A difference of electrical potential repre-sents another example. A tank of compressed gas in a room at atmospheric pressure, a vacuum tank in a similar room, a charged battery, any device that can produce high-grade energy (mechanical work) or be degraded by some irreversible process (thermal con-duction, electrical resistivity, friction, viscosity) is a source of negentropy.
3.a There is often a contradict intuition about information entropy. Shannon approach sees maximum entropy as maximum uncertainty / information.
3.b Joe Rosen in "The Symmetry Principle" states that maximum entropy is maximum symmetry – which means maximum redundancy, so minimum amount of information.
4. Non-equilibrium thermodynamics – the branch is not mature and does not serve as a tool to solve issues like in 2.a, AFAIK.
I was seeing The Physics of Maxwell's demon and information as very good guide through equilibrium (what about non-equilibrium?) thermodynamics, its connection with work and information. The authors did, however, when elaborating on entropy of a system in Brillouin's view, put an equal sign to it and Shannon entropy – which I think is contradict to Brillouin itself – who as I cited in 2.b stated that it is disequilibrium that allows system to work – meaning a complex, information-rich system (in other paragraph he also explicitly sates that negentropy is information). This conforms to Rosen 3.b.
Are there other good compilations on entropy, information, maybe complexity science? Such that solve the contradictions, form compatible non-equilibrium foundation?