\) For a continuous probability distribution with density function \(\rho\ ,\) the Gibbs entropy is defined as The formula ( 4) reduces to ( 2) if \(p_\omega = \frac 1N\) for all microstates in \(M_A\. Notice that when an element \(dQ\) of heat is transmitted from a warmer body at temperature \(T_1\) to a cooler one at temperature \(T_2\ ,\) then the entropy of the first body changes by \(-\frac p_\omega\log_2 (p_\omega). The absolute value of entropy is established by the Of each state up to a constant (which is satisfactory in most cases). The above formula allows one to compare the entropies of different states of a system, or to compute the entropy \(T\) is the absolute temperature of that body at that moment, and the integration is over all elements of heatĪctive in the passage. Where \(dQ\) denotes an element of heat being absorbed (or emitted then it has negative sign) by a body, The change of entropy of a physical system when it passes from one state to another equals In thermodynamics, a physical system is a collection of objects (bodies) whose state is parametrizedīy several characteristics such as the distribution of density, pressure, temperature, velocity, chemical potential, etc. Usually, it roughly means disorder, chaos, decay of diversity or tendency toward uniform distribution of kinds.Įntropy in physics Thermodynamical entropy - macroscopic approach The term entropy is now used in many other sciences (such as sociology), sometimes distant from physics or mathematics, where it no longer maintains its rigorous quantitative character. ![]() Maxwell (around 1871) triggered a search for the physical meaning of information, which resulted in the finding by Rolf Landauer (1961) of the heat equivalent of the erasure of one bit of information, which brought the notions of entropy in thermodynamics and information theory together. The formulation of Maxwell's paradox by James C. The concept of entropy in dynamical systems was introduced by Andrei Kolmogorov and made precise by Yakov Sinai in what is now known as the Kolmogorov-Sinai entropy. Later this led to the invention of entropy as a term in probability theory by Claude Shannon (1948), popularized in a joint book with Warren Weaver, that provided foundations for information theory. Entropy was generalized to quantum mechanics in 1932 by John von Neumann. This idea was later developed by Max Planck. The Austrian physicist Ludwig Boltzmann and the American scientist Willard Gibbs put entropy into the probabilistic setup of statistical mechanics (around 1875). The idea was inspired by an earlier formulation by Sadi Carnot of what is now known as the second law of thermodynamics. The word reveals an analogy to energy and etymologists believe that it was designed to denote the form of energy that any energy eventually and inevitably turns into - a useless heat. The term entropy was coined in 1865 by the German physicist Rudolf Clausius from Greek en- = in + trope = a turning (point).
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |