Entropy (information theory) 2 bits of entropy. A single toss of a fair coin has an entropy of one bit. A series of two fair coin tosses has an entropy of two bits. The number of fair coin tosses is its entropy in bits. This random selection between two outcomes in a sequence over time, whether the outcomes are equally probable or not, is often referred to as a Bernoulli process. The entropy of such a process is given by the binary entropy function. This definition of "entropy" was introduced by Claude E. Entropy is a measure of unpredictability of information content. Now consider the example of a coin toss. English text has fairly low entropy. If a compression scheme is lossless—that is, you can always recover the entire original message by decompressing—then a compressed message has the same quantity of information as the original, but communicated in fewer characters. Shannon's theorem also implies that no lossless compression scheme can compress all messages. . The average uncertainty , with
Entropy of an Ideal Gas, hyperphysics The entropy S of a monoatomic ideal gas can be expressed in a famous equation called the Sackur-Tetrode equation. where N = number of atoms k = Boltzmann's constant V = volume U = internal energyh = Planck's constant One of the things which can be determined directly from this equation is the change in entropy during an isothermal expansion where N and U are constant (implying Q=W). For determining other functions, it is useful to expand the entropy expression to separate the U and V dependence. Then making use of the definition of temperature in terms of entropy: This gives an expression for internal energy that is consistent with equipartition of energy. with kT/2 of energy for each degree of freedom for each atom. For processes with an ideal gas, the change in entropy can be calculated from the relationship Making use of the first law of thermodynamics and the nature of system work, this can be written then But since specific heats are related by CP = CV + R,
Entropy Figure 1: In a naive analogy, energy in a physical system may be compared to water in lakes, rivers and the sea. Only the water that is above the sea level can be used to do work (e.g. propagate a turbine). Entropy represents the water contained in the sea. In classical physics, the entropy of a physical system is proportional to the quantity of energy no longer available to do physical work. History The term entropy was coined in 1865 [Cl] by the German physicist Rudolf Clausius from Greek en- = in + trope = a turning (point). The Austrian physicist Ludwig Boltzmann [B] and the American scientist Willard Gibbs [G] put entropy into the probabilistic setup of statistical mechanics (around 1875). The concept of entropy in dynamical systems was introduced by Andrei Kolmogorov [K] and made precise by Yakov Sinai [Si] in what is now known as the Kolmogorov-Sinai entropy. The formulation of Maxwell's paradox by James C. Entropy in physics Thermodynamical entropy - macroscopic approach References
Ideal gas#entropy An ideal gas is a theoretical gas composed of a set of randomly moving, non-interacting point particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics. One mole of an ideal gas has a volume of 22.41 L at STP. The ideal gas model tends to fail at lower temperatures or higher pressures, when intermolecular forces and molecular size become important. It also fails for most heavy gases, such as many refrigerants,[1] and for gases with strong intermolecular forces, notably water vapor. At low pressures, the volume of a real gas is often considerably greater than that of an ideal gas. The ideal gas model has been explored in both the Newtonian dynamics (as in "kinetic theory") and in quantum mechanics (as a "gas in a box"). Types of ideal gas[edit] There are three basic classes of ideal gas: Classical thermodynamic ideal gas[edit] One of them is the well known ideal gas law ; that is, . .
8. Reductio ad Absurdum – A Concise Introduction to Logic 8.1 A historical example In his book, The Two New Sciences,[10] Galileo Galilea (1564-1642) gives several arguments meant to demonstrate that there can be no such thing as actual infinities or actual infinitesimals. One of his arguments can be reconstructed in the following way. He also proposes that we take as a premise that there is an actual infinity of the squares of the natural numbers. Now, Galileo reasons, note that these two groups (today we would call them “sets”) have the same size. If we can associate every natural number with one and only one square number, and if we can associate every square number with one and only one natural number, then these sets must be the same size. But wait a moment, Galileo says. We have reached two conclusions: the set of the natural numbers and the set of the square numbers are the same size; and, the set of the natural numbers and the set of the square numbers are not the same size. 8.2 Indirect proofs (P→(QvR)) This argument looks valid.
Entropy (energy dispersal) Interpretation of entropy as a measure of the spread of energy In this alternative approach, entropy is a measure of energy dispersal or spread at a specific temperature. Changes in entropy can be quantitatively related to the distribution or the spreading out of the energy of a thermodynamic system, divided by its temperature. Some educators propose that the energy dispersal idea is easier to understand than the traditional approach. Comparisons with traditional approach[edit] The term "entropy" has been in use from early in the history of classical thermodynamics, and with the development of statistical thermodynamics and quantum theory, entropy changes have been described in terms of the mixing or "spreading" of the total energy of each constituent of a system over its particular quantized energy levels. Description[edit] Current adoption[edit] History[edit] See also[edit] Introduction to entropy References[edit] Further reading[edit] Texts using the energy dispersal approach[edit]
untitled Chapter 4: Music I preface the following by the admission that I have developed little to no musical aptitude as yet and have never studied music theory. However, that does not seem to have stopped me from uncovering what looks to be some very interesting observations having applied Mod 9 to the frequencies generated by the black and white keys of the musical scale. 1955 saw the introduction of the International Standard Tuning of 440 Hz on the A of Middle C Octave. This standardised all instruments around the world. The C's were all 3 & 6, same for C sharp, then D's are all 9's and on until I came to F which revealed the 1 2 4 8 7 5 sequence, in order. You will notice that using this tuning at 440 Hz we see that: 5 sections of the octave are 1 2 4 8 7 5 4 sections are 3 & 6 3 sections are 9 Immediately the Pythagorean 3 4 5 triangle springs to mind. Above, we can clearly see that, as with the numbers, the octaves are paired up symmetrically and reflected, separated by 3 octaves. Cymatics.
Residual entropy Residual entropy is the difference in entropy between a non-equilibrium state and crystal state of a substance close to absolute zero. This term is used in condensed matter physics to describe the entropy at zero kelvin of a glass or plastic crystal referred to the crystal state, whose entropy is zero according to the third law of thermodynamics. It occurs if a material can exist in many different states when cooled. The most common non-equilibrium state is vitreous state, glass. A common example is the case of carbon monoxide, which has a very small dipole moment. As the carbon monoxide crystal is cooled to absolute zero, few of the carbon monoxide molecules have enough time to align themselves into a perfect crystal (with all of the carbon monoxide molecules oriented in the same direction). , rather than zero. Another example is any amorphous solid (glass). History[edit] One of the first examples of residual entropy was pointed out by Pauling to describe water ice. See also[edit]
The Zero Point Field: How Thoughts Become Matter? | HuffPost Life Since I have mentioned the zero point field (ZPF) so much in my past HuffPost articles, and seeing as how it is a vital component to what is going on, it only makes sense to provide a more detailed analysis for all those Quantum buffs who struggle with my theory that thoughts equal matter. So, let's start with the basics and show what is known about the ZPF, and how its discovery come about? ZPF Basics In quantum field theory, the vacuum state is the quantum state with the lowest possible energy; it contains no physical particles, and is the energy of the ground state. This is also called the zero point energy; the energy of a system at a temperature of zero. But quantum mechanics says that, even in their ground state, all systems still maintain fluctuations and have an associated zero-point energy as a consequence of their wave-like nature. Liquid helium-4 is a great example: Under atmospheric pressure, even at absolute zero, it does not freeze solid and will remain a liquid.
Entropy and life Relationship between the thermodynamic concept of entropy and the evolution of living organisms Research concerning the relationship between the thermodynamic quantity entropy and both the origin and evolution of life began around the turn of the 20th century. In 1910, American historian Henry Adams printed and distributed to university libraries and history professors the small volume A Letter to American Teachers of History proposing a theory of history based on the second law of thermodynamics and on the principle of entropy.[1][2] Ideas about the relationship between entropy and living organisms have inspired hypotheses and speculations in many contexts, including psychology, information theory, the origin of life, and the possibility of extraterrestrial life. Early views[edit] where entropy absolute temperature McCulloh gives a few of what he calls the "more interesting examples" of the application of these laws in extent and utility. Negative entropy[edit] Gibbs free energy Where and