Category:Thermodynamic entropy. Quantum mechanical entropy.
Ideal Gas Entropy. Bekenstein bound. Upper limit on entropy in physics Equations[edit] where S is the entropy, k is the Boltzmann constant, R is the radius of a sphere that can enclose the given system, E is the total mass–energy including any rest masses, ħ is the reduced Planck constant, and c is the speed of light. Note that while gravity plays a significant role in its enforcement, the expression for the bound does not contain the gravitational constantG, and so, it ought to apply to quantum field theory in curved spacetime.
The Bekenstein–Hawking boundary entropy of three-dimensional black holes exactly saturates the bound. And so the two-dimensional area of the black hole's event horizon is and using the Planck length the Bekenstein–Hawking entropy is One interpretation of the bound makes use of the microcanonical formula for entropy, where is the number of energy eigenstates accessible to the system. Origins[edit] Bekenstein derived the bound from heuristic arguments involving black holes. For some constant. . , entropy . . . Boltzmann's entropy formula. Equation in statistical mechanics In statistical mechanics, Boltzmann's equation (also known as the Boltzmann–Planck equation) is a probability equation relating the entropy , also written as or where is the Boltzmann constant (also written as simply ) and equal to 1.380649 × 10−23 J/K, and is the natural logarithm function (also written as , as in the image above).
In short, the Boltzmann formula shows the relationship between entropy and the number of ways the atoms or molecules of a certain kind of thermodynamic system can be arranged. History[edit] The equation was originally formulated by Ludwig Boltzmann between 1872 and 1875, but later put into its current form by Max Planck in about 1900.[2][3] To quote Planck, "the logarithmic connection between entropy and probability was first stated by L. There are many instantaneous microstates that apply to a given macrostate. Where i ranges over all possible molecular conditions and "! " Introduction of the Natural Logarithm[edit] Boltzmann used a. Configuration entropy. From Wikipedia, the free encyclopedia Measure of particle positions within a system In statistical mechanics, configuration entropy is the portion of a system's entropy that is related to discrete representative positions of its constituent particles. For example, it may refer to the number of ways that atoms or molecules pack together in a mixture, alloy or glass, the number of conformations of a molecule, or the number of spin configurations in a magnet.
The name might suggest that it relates to all possible configurations or particle positions of a system, excluding the entropy of their velocity or momentum, but that usage rarely occurs.[1] Calculation[edit] If the configurations all have the same weighting, or energy, the configurational entropy is given by Boltzmann's entropy formula where kB is the Boltzmann constant and W is the number of possible configurations. See also[edit] Notes[edit] References[edit] Conformational entropy. From Wikipedia, the free encyclopedia Entropy associated with a molecule's possible conformations where R is the gas constant and pi is the probability of a residue being in rotamer i.[3] The limited conformational range of proline residues lowers the conformational entropy of the denatured state and thus stabilizes the native states.
A correlation has been observed between the thermostability of a protein and its proline residue content.[4] See also[edit] References[edit] Depletion force. Effective force in molecular and colloidal systems A depletion force is an effective attractive force that arises between large colloidal particles that are suspended in a dilute solution of depletants, which are smaller solutes that are preferentially excluded from the vicinity of the large particles.[1][2] One of the earliest reports of depletion forces that lead to particle coagulation is that of Bondy, who observed the separation or "creaming" of rubber latex upon addition of polymer depletant molecules (sodium alginate) to solution.[3] More generally, depletants can include polymers, micelles, osmolytes, ink, mud, or paint dispersed in a continuous phase.[1][4] Causes[edit] Sterics[edit] The system of colloids and depletants in solution is typically modeled by treating the large colloids and small depletants as dissimilarly sized hard spheres.[1] Hard spheres are characterized as non-interacting and impenetrable spheres.
Hard-sphere potential[edit] and depletant sols of diameter is: is . Disgregation. 1862 formulation of the concept of entropy Historical context[edit] In 1824, French physicist Sadi Carnot assumed that heat, like a substance, cannot be diminished in quantity and that it cannot increase. Specifically, he states that in a complete engine cycle ‘that when a body has experienced any changes, and when after a certain number of transformations it returns to precisely its original state, that is, to that state considered in respect to density, to temperature, to mode of aggregation, let us suppose, I say that this body is found to contain the same quantity of heat that it contained at first, or else that the quantities of heat absorbed or set free in these different transformations are exactly compensated.’
Furthermore, he states that ‘this fact has never been called into question’ and ‘to deny this would overthrow the whole theory of heat to which it serves as a basis.’ Definition[edit] Clausius introduced disgregation in the following passage: Verbal justification[edit] Ectropy. Measure of distance to normality In a note to What is Life? Schrödinger explained his use of this phrase. ... if I had been catering for them [physicists] alone I should have let the discussion turn on free energy instead.
It is the more familiar notion in this context. But this highly technical term seemed linguistically too near to energy for making the average reader alive to the contrast between the two things. Information theory[edit] Negentropy is defined as where is the differential entropy of the Gaussian density with the same mean and variance as and is the differential entropy of Negentropy is used in statistics and signal processing. The negentropy of a distribution is equal to the Kullback–Leibler divergence between and a Gaussian distribution with the same mean and variance as (see Differential entropy § Maximization in the normal distribution for a proof).
Correlation between statistical negentropy and Gibbs' free energy[edit] where: is entropy is the Massieu potential energy. Entropic explosion. From Wikipedia, the free encyclopedia An entropic explosion is an explosion in which the reactants undergo a large change in volume without releasing a large amount of heat. The chemical decomposition of triacetone triperoxide (TATP) may be an example of an entropic explosion.[1] It is not a thermochemically highly favored event because little energy is generated in chemical bond formation in reaction products, but rather involves an entropy burst, which is the result of formation of one ozone and three acetone gas phase molecules from every molecule of TATP in the solid state.[2][3][4][5] This hypothesis has been questioned as opposing to other theoretical investigations as well as actual measurements of the detonation heat of TATP.
Experiments have shown that the explosion heat of TATP is about 2800 kJ/kg (about 70% of TNT) and that it acts as a usual explosive, producing a mix of hydrocarbons, water and carbon oxides upon detonation.[6] Entropic force. Physical force that originates from thermodynamics instead of fundamental interactions In physics, an entropic force acting in a system is an emergent phenomenon resulting from the entire system's statistical tendency to increase its entropy, rather than from a particular underlying force on the atomic scale.[1][2] Mathematical formulation[edit] In the canonical ensemble, the entropic force associated to a macrostate partition is given by[3] where is the temperature, is the entropy associated to the macrostate , and is the present macrostate.[4] Examples[edit] Pressure of an ideal gas[edit] The internal energy of an ideal gas depends only on its temperature, and not on the volume of its containing box, so it is not an energy effect that tends to increase the volume of the box as gas pressure does.
Brownian motion[edit] The entropic approach to Brownian movement was initially proposed by R. Polymers[edit] Hydrophobic force[edit] Colloids[edit] Cytoskeleton[edit] Controversial examples[edit] Gravity[edit] Entropy (classical thermodynamics) Measure of disorder within thermodynamic systems Ludwig Boltzmann explained the entropy as a measure of the number of possible microscopic configurations Ω of the individual atoms and molecules of the system (microstates) which correspond to the macroscopic state (macrostate) of the system. He showed that the thermodynamic entropy is k ln Ω, where the factor k has since been known as the Boltzmann constant. Concept[edit] Differences in pressure, density, and temperature of a thermodynamic system tend to equalize over time.
For example, in a room containing a glass of melting ice, the difference in temperature between the warm room and the cold glass of ice and water is equalized by energy flowing as heat from the room to the cooler ice and water mixture. Over time, the temperature of the glass and its contents and the temperature of the room achieve a balance. Definition[edit] With being the uniform temperature of the closed system and That means the line integral is path-independent. so that. 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. The concept has been used to facilitate teaching entropy to students beginning university chemistry and biology. 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] Entropy (order and disorder) Interpretation of entropy as the change in arrangement of a system's particles In the years to follow, Ludwig Boltzmann translated these 'alterations of arrangement' into a probabilistic view of order and disorder in gas-phase molecular systems. In the context of entropy, "perfect internal disorder" has often been regarded as describing thermodynamic equilibrium, but since the thermodynamic concept is so far from everyday thinking, the use of the term in physics and chemistry has caused much confusion and misunderstanding.
History[edit] Overview[edit] To highlight the fact that order and disorder are commonly understood to be measured in terms of entropy, below are current science encyclopedia and science dictionary definitions of entropy: The mathematical basis with respect to the association entropy has with order and disorder began, essentially, with the famous Boltzmann formula, The entropy of the universe tends to a maximum. Phase change[edit] Entropy-driven order[edit] See also[edit] Entropy (statistical thermodynamics) Concept The concept entropy was first developed by German physicist Rudolf Clausius in the mid-nineteenth century as a thermodynamic property that predicts that certain spontaneous processes are irreversible or impossible. In statistical mechanics, entropy is formulated as a statistical property using probability theory.
The statistical entropy perspective was introduced in 1870 by Austrian physicist Ludwig Boltzmann, who established a new field of physics that provided the descriptive linkage between the macroscopic observation of nature and the microscopic view based on the rigorous treatment of large ensembles of microstates that constitute thermodynamic systems. Boltzmann's principle[edit] Ludwig Boltzmann defined entropy as a measure of the number of possible microscopic states (microstates) of a system in thermodynamic equilibrium, consistent with its macroscopic thermodynamic properties, which constitute the macrostate of the system.
Gibbs entropy formula[edit] The quantity where. 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. Entropy as an arrow of time. Use of the second law of thermodynamics to distinguish past from future Much like temperature, despite being an abstract concept, everyone has an intuitive sense of the effects of entropy.
For example, it is often very easy to tell the difference between a video being played forwards or backwards. A video may depict a wood fire that melts a nearby ice block; played in reverse, it would show a puddle of water turning a cloud of smoke into unburnt wood and freezing itself in the process. Surprisingly, in either case, the vast majority of the laws of physics are not broken by these processes, with the second law of thermodynamics being one of the only exceptions. When studying at a microscopic scale, the above judgements cannot be made. Overview[edit] The second law of thermodynamics allows for the entropy to remain the same regardless of the direction of time. An example of apparent irreversibility[edit] Mathematics of the arrow[edit] which equals: Correlations[edit] , where Cosmology[edit] Entropy in thermodynamics and information theory.
Entropy of fusion. Entropy of mixing. Entropy of vaporization. Free entropy. Geometrical frustration. H-theorem. Heat death of the universe. High-entropy alloy. High-entropy-alloy nanoparticles. History of entropy. Homentropic flow. Introduction to entropy. Isentropic nozzle flow. Isentropic process. Landauer's principle. Loop entropy. Maximum entropy thermodynamics. Negentropy. Nonextensive entropy. Nucleate boiling. Residual entropy. Sackur–Tetrode equation. Standard molar entropy. Tsallis entropy. SECT3 Entropy and Classical Thermodynamics. Ideal gas#entropy. Entropy of an Ideal Gas, hyperphysics. Entropy - s243a.wikispaces. Entropy, wikipedia. Carnot cycle. Entropy of fusion.
Entropy (Information Theory) Entropy of Mixing. Reduced Entropy. Entropy (Statistical Mechanics) Second law of thermodynamics. Entropy of vaporization. State function. Entropy (Dynamical Systems) Statistical Mechanics. Thermodynamic State Variables. Thermodynamics. Physics.