Arnold's cat map as ordered chaos?

"Most biological processes work to keep the entropy in your body low, at the expense of increasing the entropy around you."

http://physics.stackexchange.com/questions/54493/entropy-and-crystal-growth

The third law of thermodynamics is sometimes stated as follows, regarding the properties of systems in equilibrium at absolute zero temperature:

The entropy of a perfect crystal at absolute zero is exactly equal to zero.

At absolute zero (zero kelvin), the system must be in a state with the minimum possible energy, and the above statement of the third law holds true provided that the perfect crystal has only one minimum energy state. Entropy is related to the number of accessible microstates, and for a system consisting of many particles, quantum mechanics indicates that there is only one unique state (called the ground state) with minimum energy. If the system does not have a well-defined order (if its order is glassy, for example), then in practice there will remain some finite entropy as the system is brought to very low temperatures as the system becomes locked into a configuration with non-minimal energy. The constant value is called the residual entropy of the system.

The Nernst–Simon statement of the third law of thermodynamics concerns thermodynamic processes at a fixed, low temperature:

The entropy change associated with any condensed system undergoing a reversible isothermal process approaches zero as the temperature at which it is performed approaches 0 K.

Here a condensed system refers to liquids and solids. A classical formulation by Nernst (actually a consequence of the Third Law) is:

It is impossible for any process, no matter how idealized, to reduce the entropy of a system to its absolute-zero value in a finite number of operations.

http://en.wikipedia.org/wiki/Third_law_of_thermodynamics Physically, the Nernst–Simon statement implies that it is impossible for any procedure to bring a system to the absolute zero of temperature in a finite number of steps.

"Entropy is a measure of the disorder of a system. That disorder can be represented in terms of energy that is not available to be used. Natural processes will always proceed in the direction that increases the disorder of a system. When two objects are at different temperatures, the combined systems represent a higher sense of order than when they are in equilibrium with each other. The sense of order is associated with the atoms of system A and the atoms of system B being separated by average energy per atom - those of A being the higher energy atoms if system A is at a higher temperature. When they are put in thermal contact, energy flows from the higher average energy system to the lower average energy system to make the energy of the combined system more uniformly distributed - ie, less ordered. So the disorder of the system has increased - and we say the entropy has increased. But the process of increasing the disorder has removed the possibility that the energy that was transferred from A to B can be used for any other purpose - for example, work cannot be extracted from the energy by operating a heat engine between the two reservoirs of different temperatures. So although energy was conserved in the transfer (the first law), the entropy of the universe has increased in becoming more disordered (the second law) and consequently the availability of energy for doing work has decreased."

http://www.calpoly.edu/~rbrown/entropy.html

"The principle of maximum entropy states that, subject to precisely stated prior data (such as a proposition that expresses testable information), the probability distribution which best represents the current state of knowledge is the one with largest entropy.

Another way of stating this: Take precisely stated prior data or testable information about a probability distribution function. Consider the set of all trial probability distributions that would encode the prior data. Of those, the one with maximal information entropy is the proper distribution, according to this principle."

http://en.wikipedia.org/wiki/Principle_of_maximum_entropy

"In a world governed by the second law of thermodynamics, all isolated systems are expected to approach a state of maximum disorder. Since life approaches and maintains a highly ordered state, some argue that this seems to violate the aforementioned Second Law implicating a paradox. However, since life is not an isolated system, there is no paradox. The increase of order inside an organism is more than paid for by an increase in disorder outside this organism. By this mechanism, the Second Law is obeyed, and life maintains a highly ordered state, which it sustains by causing a net increase in disorder in the Universe. In order to increase the complexity on Earth — as life does — energy is needed. Energy for life here on Earth is provided by the Sun."