For example, the notion of gauge invariance forms the basis of the well-known Mattis spin glasses, which are systems with the usual spin degrees of freedom for i = 1 ,..., N, with the special fixed " random " couplings Here the ε < sub > i </ sub > and ε < sub > k </ sub > quantities can independently and " randomly " take the values ± 1, which corresponds to a most-simple gauge transformation This means that thermodynamic expectation values of measurable quantities, e. g. of the energy are invariant.

For processes that involve only suitably small and smooth spatial inhomogeneities and suitably small changes with time, a good approximation can be found through the assumption of local thermodynamic equilibrium.

For a given physical process, the selection of suitable independent local non-equilibrium macroscopic state variables for the construction of a thermodynamic description calls for qualitative physical understanding, rather than being a simply mathematical problem concerned with a uniquely determined thermodynamic description.

For example, according to Callen, " in absolute thermodynamic equilibrium all radioactive materials would have decayed completely and nuclear reactions would have transmuted all nuclei to the most stable isotopes.

For a fluid in thermodynamic equilibrium, the stress-energy tensor takes on a particularly simple form

For cytochrome c and some other proteins, it has been shown that the molten globule state is a " thermodynamic state " clearly different both from the native and the denatured state, demonstrating for the first time the existence of a third equilibirum ( i. e., intermediate ) state.

For example, for a car engine, apart from friction and thermodynamic losses inside to the engine, power is absorbed by the, alternator, and radiator fan, thus reducing the power available at the flywheel to move the car along.

For a particular reversible process in general, the work done reversibly on the system,, and the heat transferred reversibly to the system, are not required to occur respectively adiabatically or adynamically, but they must belong to the same particular process defined by its particular reversible path,, through the space of thermodynamic states.

For example, local thermodynamic equilibrium in a liquid is reached within a few collision times.

For homogeneous substances, these extensive thermodynamic properties each have analogous intensive thermodynamic properties, which can be expressed on a per mass basis, and the corresponding intensive property symbols would be the lower case letters of the corresponding extensive property.

For example, in the infinitesimal expression, the contractile work energy associated with a thermodynamic system that is a contractile fiber that shortens by an amount − dl under a force f would result in a term fdl being added.

For a given material or substance, the standard state is the reference state for the material's thermodynamic state properties such as enthalpy, entropy, Gibbs free energy, and for many other material standards.

For such a system, the negative of the difference in the Helmholtz energy is equal to the maximum amount of work extractable from a thermodynamic process in which temperature and volume are held constant.

For their macroscopic thermodynamic account of phenomena, they started by accepting, on empirical physical grounds, the presupposed notions of thermal insulation, thermal contact, and thermal equilibrium ( page 56 ).

* For a completely isolated system, S is maximum at thermodynamic equilibrium.

* For a system with controlled constant temperature and volume, A is minimum at thermodynamic equilibrium.

* For a system with controlled constant temperature and pressure, G is minimum at thermodynamic equilibrium.

For example, internal energy, enthalpy, and entropy are state quantities because they describe quantitatively an equilibrium state of a thermodynamic system, irrespective of how the system arrived in that state.

For example, in the atmosphere, the speed of sound is much greater than the wind speed ; this favours the idea of local thermodynamic equilibrium of matter for atmospheric heat transfer studies at altitudes below about 60 km where sound propagates, but not above 100 km, where, because of the paucity of intermolecular collisions, sound does not propagate.

For the above example, kinetic control may be established with LDA at − 78 ° C, giving 99: 1 selectivity of kinetic: thermodynamic enolate, while thermodynamic control may be established with triphenylmethyllithium at room temperature, giving 10: 90 selectivity.

For example, it predicts that every molecule in a monoatomic ideal gas has an average kinetic energy of ( 3 / 2 ) k < sub > B </ sub > T in thermal equilibrium, where k < sub > B </ sub > is the Boltzmann constant and T is the ( thermodynamic ) temperature.

For any pencil in a plane containing a Af-fold secant of **zg has an image regulus which meets the plane of the pencil in Af lines, namely the images of the lines of the pencil which pass through the intersection of **zg and the multiple secant, plus an additional component to account for the intersections of the images of the general lines of the pencil.

For hundreds of years, the evidence available consisted of ( 1 ) the captain's fragmentary journal, ( 2 ) a highly prejudiced account by one of the survivors, ( 3 ) a note found in a dead man's desk on board, and ( 4 ) several second-hand reports.

For this does not account for the integral, elemental power of that which grows with abounding vigor as the play unfolds, nor does it explain the strange numinous sense of presentness which comes over those who watch the play like a spell.

For in Christ Jesus neither circumcision nor uncircumcision but a new creation is of any account.

For much more distant objects the Euclidean approximation is not valid, and General Relativity must be taken into account when calculating the luminosity distance of an object.

For 160 years Wirt's account was taken at face value.

For example the entries in the Sales Journal are taken and a debit entry is made in each customer's account ( showing that the customer now owes us money ) and a credit entry might be made in the account for " Sale of class 2 widgets " ( showing that this activity has generated revenue for us ).

For example, the " inventory " account asset account might be changed to bring them into line with the actual numbers counted during a stock take.

For incumbent management, the contrary views of some of their members were not matters to be weighed in the balance and taken account of in formulation of policy.

For an atemporal interpretation that “ makes no attempt to give a ‘ local ’ account on the level of determinate particles ”, the conjugate wavefunction, (" advanced " or time-reversed ) of the relativistic version of the wavefunction, and the so-called " retarded " or time-forward version are both regarded as real and the transactional interpretation results.

For example, in one of the Four Great Classical Novels of China, The Dream of the Red Chamber ( believed to be a semi-autobiographical account of author Cao Xueqin's own family life ), three generations of the Jia family are supported by one favorite concubine of the Emperor.

" For Adorno and Horkheimer, this posed the problem of how to account for the apparent persistence of domination in the absence of the very contradiction that, according to traditional critical theory, was the source of domination itself.

* For a more detailed account of Christine de Pizan ’ s rhetorical strategies refer to Jenny R. Redfern ’ s excerpt Christine de Pisan and The Treasure of the City of Ladies: A Medieval Rhetorician and Her Rhetoric ( in Reclaiming Rhetorica, ed.

For numerical calculations, it is important to take account of the characteristics of the arithmetic.

* Technological progress — For over a century, economists have known that capital and labor do not account for all of economic growth.

For some of the ancient sources, such as Herophilus, Galen's account of their work is all that survives.

For example, it is quite common for works of moral instruction to have an imaginative setting, as a means of getting the audience's attention, but it is difficult to see how Hesiod could have travelled the countryside entertaining people with a narrative about himself if the account was known to be fictitious.

For Habakkuk, however, there is no reliable account of any of these.

For example, Joseph Goering of the University of Toronto has identified sources for Grail imagery in 12th century wall paintings from churches in the Catalan Pyrenees ( now mostly removed to the Museu Nacional d ' Art de Catalunya, Barcelona ), which present unique iconic images of the Virgin Mary holding a bowl that radiates tongues of fire, images that predate the first literary account by Chrétien de Troyes.

For the past hundred years there has been an abundance of evidence that psychological and physiological changes could be produced by hypnotism which were worth study on their own account, and also that such changes might be of great service in the treatment of patients.

For instance, David Ricardo theorized that prices are determined by the amount of labor but found exceptions for which the labor theory could not account.

For example, one might argue that the myth of the wind-god Aeolus evolved from a historical account of a king who taught his people to use sails and interpret the winds.

For example, in a pure cash deal ( financed from the company ’ s current account ), liquidity ratios might decrease.