... and shall eat your flesh as it were fire.
Entropy - and shall eat your flesh as it were fire Your riches are corrupted, and your garments are motheaten. Your gold and silver is cankered; and the rust of them shall be a witness against you, and shall eat your flesh as it were fire. Ye have heaped treasure together for the last days. Behold, the hire of the labourers ...
James 5:2-4
Entropy has profound implications in all areas of physics: mechanical, chemical, electrical, and even biology and life. If I knew the artist's name that drew this wonderful picture, I would give full credit. This picture exemplifies the verse from the Great Book, emphasizing thermodynamic-like events as a common denominator of all other entropies.

I will continue a discussion of Entropy as only applied to thermodynamics.

I have shown the macroscopic and the microscopic view of heat to be describing the same thing.

First Law of thermodynamics:

Conservation of energy is time symmetric. Energy is conserved forward or backward in time: no time (no past and no future).

Second Law of thermodynamics:

Entropy dictates the flow of heat between two systems, involving time asymmetry.
Entropy is a trend.
Entropy is a measure of a system's tendency towards change in energy distribution.

Entropy is closely related to energy dissipation, and sometimes described as dispersal. Any global (closed system) change is never reversable, and that change always represents an increase in entropy. Also, time has a direction. Entropy represents the amount of useful, capitalizable, profitable, work. This definition depends on the temperature difference, and leads directly to the units of entropy: Energy divided by Temperature, Joule(J) per degree(K), Joule per Kelvin (J K-1).
EqEntropyE.gif, 2 kB
Heat energy involved in a transformation
divided by the absolute temperature.
EqEntropyS.gif, 1 kB
Entropy is denoted by a symbol: S.
Entropy is the amount of energy (or heat) that has moved, or spread out; or changed state, or position, dispersion, or representation.
Infinitesimal small amount of heat dE
In thermodynamics, it is the amount of heat energy involved in a transformation divided by the absolute temperature.

Work-Q1Q2.jpg, 8 kB
A carnot engine...
Heat from one reservor flows through the engine and into a sink reservor.

Work is usually in the form of coherent motion, such as moving a piston. Work is usually in the form of mechanical energy, and can be kinetic or potential.
Eq-WQQ.gif, 1 kB

Eq-Nu-W.gif, 2 kB
Eq-Nu-Q.gif, 2 kB
Substituting from above...
Efficiency in terms of Q

Eq-Nu-T.gif, 2 kB
The maximum possible Efficiency.
T1 is the initial Hot temperature.

Entropy is a useful measure of how much energy is available for useful work, such as mechanical or kinetic energy. For example, consider the worlds oceans. There is so much energy here in the form of heat, but it can not be used because there is no colder source into which that heat energy could flow.

EqEfficiency.gif, 2 kB
Carnot Efficiency:
The maximum possible temperature efficiency with perfect mechanical design.
This figure is a percentage, and represents the epidemy of entropy, a similar concept.

EqEntropyTinstant.gif, 2 kB
Integral of
element of heat: ElementofHeat.gif, 0 kB d(E)
divided by
instantaneous temperature: T
Entropy is a measure of energy dispersal at a specific temperature.
Entropy is a spreading out of energy in reference to an equilibrium base.
Entropy is a probabilistic property.

CoffeeToMatt.jpg, 42 kB EqHeatCap.gif, 2 kB

BBALLBLU.GIF, 0 kB A cup of coffee starts out at 200F degrees, 366.5K .

BBALLBLU.GIF, 0 kB Specific heat for water (coffee):
1 calorie/gram C = 4.186 joule/gram/C
4.186 kJ kg-1 K-1.

BBALLBLU.GIF, 0 kB 12oz of coffee = .34kg

BBALLBLU.GIF, 0 kB Ambient Media equilibrium temperature: T(M) = 70F, 294.3K

BBALLYEL.GIF, 0 kB Carnot max Efficiency = 19.7%

BBALLRED.GIF, 0 kB 302.2 J Heat transferred, displaced, moved to different position.

EqEntropyAprox.gif, 4 kB
As a very quick approximation...
T(M)= Temperature of media at equilibrium in kelvin.
T(H)= Temperature of Hot coffee in kelvin.
BBALLGRN.GIF, 0 kB S = +0.915 J/K Entropy
Rough approximation

EqEntropyIntr.gif, 2 kB EqEntropyInt2.gif, 5 kB
But using the Integral form:
T(M)= Temperature of media at equilibrium
in kelvin.
T(H)= Temperature of Hot coffee.
BBALLGRN.GIF, 0 kB S = +0.918 J/K Entropy

EqEntropyCold.gif, 5 kB
For the energy going the other way...
For the energy to come out of the media
and go into the coffee cup is very unlikely.
But this is what it looks like:
Put the Source heat value at the top of the integral
and the "into" on the bottom.
The resulting entropy value is negative!
An isolated negative entropy is unlikely.
But, in very small areas, in small amounts, it is probable. Because you are breathing and reading this, it has - for sure - happened.

EqEntropySum.gif, 3 kB EqEntropySumFin.gif, 2 kB
For a closed system:
For example, create a second coffee cup.
And connect the two cups together, (in contact with one another).
Entropies may be added extrinsically.

T(H)= Temperature of Hot coffee in cup1, initial condition.
T(M)= Temperature of composit cups at equilibrium, final condition.
T(C)= Temperature of Cold coffee in cup2, initial condition.

T(M) may be involved to calculate with different volumes and different heat capacities.

EqEnergyPV.gif, 3 kB
Here is a more complete form:
With the addition of the energy: PV

EqEntropyMicro.gif, 3 kB

Microstates are the numerical number of quantum mechanical states, or ways, that molecules can differ in their energy distributions in a macro system. Thanks to Planck, there are quadrillions of energy levels in a substance. The Gibbs energy, G, can be described as "dispersible energy".

EqEntropyVolume.gif, 3 kB

If the volume is compressed, the entropy is negative. If the pressure is relaxed obtaining greater volume, greater entropy.

If a gas is quarantined in a corner of a box with a partition, and then the partition is removed, the gas will disperse according to entropy. Same temperature. Inversely: Less pressure, and more volume. Same PV energy. When you look at the universe outside the box, the entropy has not changed: Entropy change is zero!

Anam8F.gif, 222 kB

Here is an idealized frictionless system, that I conjured.
It keeps going forever, as you can see.
Heat is produced at the bottom from compression.
Cooling is produced at the top from expansion.
Compression and expansion are both "restoring" forces, and the thing oscillates.
No heat is escaping and no heat is entering.
The internal heat produced is balanced by the internal cooling.
The universe sees no change in entropy.
At any instance, the total energy is the same.

RULERMAR.GIF, 1 kB According to others, the overall universe can have a entropy of zero or positive. And that is all! Only those two values. Personally, I don't believe this at all. Most do agree with me that inside any OPEN subsystem the entropy can be increasing or decreasing or staying the same. All three! Clearly, and especially if you are reading this, NO ONE should deny this fact. However, trust in Man, and you are a fool!

While we look not at the things which are seen, but at the things which are not seen: for the things which are seen are temporal; but the things which are not seen are eternal.
2 Corinthians 4:18
The life of entropy depends upon time, and more explicitly the "direction of time". I have shown on my Time Dilation page that time stops at the edge of a black hole. It is just one example of a complete breakdown of time and entropy. There is nothing preventing matter creation at the center of our galaxy, and the formation of negative entropy. Negative entropy is present all around us, and is why we live and breathe. It is how these letters are printed and how you are reading this. Clearly, positive entropy predominates, but is not exclusive, thruout our "visible" galaxy, and hence, thruout our "visible" experience.

The b