In the experiment, the spin system is initially perturbed into a non-equilibrium state ( high " H " ), and, as predicted by the " H " theorem the quantity " H " soon decreases to the equilibrium value.
32.
In the 1970s he showed the equivalence in quantum thermodynamics of, on the one hand, the KMS ( Kubo-Martin-Schwinger ) condition for the characterization of quantum mechanical states in thermodynamic equilibrium with, on the other hand, the variational principle for quantum mechanical spin systems on lattices.
33.
In the quantum mechanical description of electron and nuclear spin systems that have a limited number of possible states, and therefore a discrete upper limit of energy they can attain, it is possible to obtain a negative temperature, which is numerically indeed less than absolute zero.
34.
Let us first move away from a gas to an idealized spin system, i . e . a solid whose consituents ( atoms ) store their ( thermal ) energy not by vibrating ( i . e ., no phonons in my model ) but by being excited.
35.
In the absence of a magnetic field, such a two-spin system would have maximum entropy when half the atoms are in the spin-up state and half are in the spin-down state, and so one would expect to find the system with close to an equal distribution of spins.
36.
For example, "'AB "'indicates two nuclei which have similar chemical shifts ( ?? similar to or smaller than J ), whereas "'AX "'indicates two which lie further apart on the spectrum ( ?? significantly larger than J ) . "'A 2 B "'would similarly indicate a spin system containing two equivalent nuclei ( A ) and a third, inequivalent one ( B ).
37.
In the case of a two spin system as described above, we can distinguish two types of pulses : soft or spin-selective pulses, whose frequency range encompasses one of the resonant frequencies only, and therefore affects only that spin; and hard or nonselective pulses whose frequency range is broad enough to contain both resonant frequencies and therefore these pulses couple to both spins.
38.
The loss of phase coherence in the transverse plane is called transverse or " T " 2 relaxation . " T " 1 is thus associated with the enthalpy of the spin system, or the number of nuclei with parallel versus anti-parallel spin . " T " 2 on the other hand is associated with the entropy of the system, or the number of nuclei in phase.
