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Thank you so much for your replies! You have both made my point, i.e. that many if not most people view entropy only from the thermodynamics.

To get a comprehensive view of "entropy" one must move beyond Clausius and also examine Maxwell, Boltzman, Gibbs, Shannon, Kolmogorov and others. Dictionary of the History of Ideas: Entropy

Revisting information entropy (logical entropy - Shannon and algorithmic entropy - Kolmogorov) here are some alternative approaches related to biological systems:

Schneider: Channel Capacity for Molecular Machines and Energy Dissipation from Molecular Machines

Divergence and Shannon Information in Genomes

Adami: Information Theory and Molecular Biology

Spunkets, the first link above goes to your inquiry into bits gained dissipating energy into the local surroundings in molecular machines.

Here are a few sample applications of the theories, illustrating the relevance to molecular biology:

A cellular automata study of constraints (dissolvence) in a perculating many-particle system

Differential Shannon entropy analysis identifies molecular property descriptors that predict aqueous solubility of synthetic compounds with high accuracy in binary QSAR calculations.

Analysis of symbolic sequences using the Jensen-Shannon divergence

Complexity of Protein-Protein Interaction networks and pathways

Thanks for the links. My post was made to distingush between thermodynamic entropy and the others. I called those engineering entropy. They are called entropy, because they have the same functional form as the thermodynamic entropy. They are both logs of the number of states accessible. The accessible states are the ones with high probability of being occupied.

Living systems are those which utilize energy to maintain themselves, grow, reproduce, move, respirate, feed, ect. Gibbs free energy is what drives these processes. dS isn't an important focus, because the reactions themselves are taking that Gibbs free energy. They are the most probable sink for the energy. They are the accessible states.

The use of Shannon entropy is for looking at the processes utilizing Gibbs free energy for productive purposes, those that are unique to life. There are also nonproductive channels, but they must consume less energy overall for life to continue. The accessible states for Shannon entropy are all possible states beforehand. Once energy has been expended, the result defines the state and is used to calculate the entropy. In the simplest case the before entropy is log(2)(a reaction might occur, or it might not), after the reaction it is log(1). As long as Gibbs energy flows though the Shannon "channels", this entropy is reduced.

Unlike energy release in bulk mixes, release in living cells occurs at collections of objects configured to capture that energy. The creation of each of those objects, their assembly and the function they serve, are all considered Shannon information. The information is ultimately coded in RNA and DNA. Once the Gibbs flow fails in key channels of information, the organism reverts to a bulk mix and Shannon entropy no longer applies. The organism is dead.

" The objection to evolution based on the Second Law of Thermodynamics will not be complete until we have thoroughly explained the thought experiment raised by betty boop on another thread:

Take a live albatross, a dead albatross and a 12 lb cannonball to the top of the Leaning Tower of Pisa and toss them over the side.

What happens next, i.e. the live albatross flying away, is what must be addressed before anyone can put the appeal to the Second Law of Thermodynamics in the "out" basket."

Bird's flap their wings and fly, or try to, when they sense the acceleration. The immune system is an unconscious reaction to life threats also. The organism begins shortly after birth to distinguish self from other, in terms of proteins and other antigens. Both reactions are coded in the DNA and involve feedback. The feedback and triggers are switches, rather than equilibrium. That is not common in chemical mixes.

It's the properties of RNA and DNA itself, the transcription reactions and their creation of catalytic machines that overcame the second law. If it can happen, it will.