There is also an asymptotic result for systems which are in a nonequilibrium steady state at all times. There is a crucial point in the fluctuation theorem, that differs from how Loschmidt framed the paradox.
Loschmidt considered the probability of observing a single trajectory, which is analogous to enquiring about the probability of observing a single point in phase space. In both of these cases the probability is always zero. To be able to effectively address this you must consider the probability density for a set of points in a small region of phase space, or a set of trajectories.
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The fluctuation theorem considers the probability density for all of the trajectories that are initially in an infinitesimally small region of phase space. This leads directly to the probability of finding a trajectory, in either the forward or the reverse trajectory sets, depending upon the initial probability distribution as well as the dissipation which is done as the system evolves. It is this crucial difference in approach that allows the fluctuation theorem to correctly solve the paradox.
Another way of dealing with Loschmidt's paradox is to see the second law as an expression of a set of boundary conditions, in which our universe's time coordinate has a low-entropy starting point: From this point of view, the arrow of time is determined entirely by the direction that leads away from the Big Bang, and a hypothetical universe with a maximum-entropy Big Bang would have no arrow of time. The theory of cosmic inflation tries to give reason why the early universe had such a low entropy.
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Third law of thermodynamics - Wikipedia
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Lewis and Merle Randall in Some crystals form defects which cause a residual entropy. This residual entropy disappears when the kinetic barriers to transitioning to one ground state are overcome. With the development of statistical mechanics , the third law of thermodynamics like the other laws changed from a fundamental law justified by experiments to a derived law derived from even more basic laws. The basic law from which it is primarily derived is the statistical-mechanics definition of entropy for a large system:.
The counting of states is from the reference state of absolute zero, which corresponds to the entropy of S 0. In simple terms, the third law states that the entropy of a perfect crystal of a pure substance approaches zero as the temperature approaches zero. The alignment of a perfect crystal leaves no ambiguity as to the location and orientation of each part of the crystal.
As the energy of the crystal is reduced, the vibrations of the individual atoms are reduced to nothing, and the crystal becomes the same everywhere. The third law provides an absolute reference point for the determination of entropy at any other temperature. The entropy of a closed system, determined relative to this zero point, is then the absolute entropy of that system.
The difference is zero, hence the initial entropy S 0 can be any selected value so long as all other such calculations include that as the initial entropy.
Let's assume the crystal lattice absorbs the incoming photon. There is a unique atom in the lattice that interacts and absorbs this photon.
So after absorption, there is N possible microstates accessible by the system, each of the microstates corresponding to one excited atom, and the other atoms remaining at ground state. The entropy, energy, and temperature of the closed system rises and can be calculated. The entropy change is:. A single atom was assumed to absorb the photon but the temperature and entropy change characterizes the entire system. An example of a system which does not have a unique ground state is one whose net spin is a half-integer, for which time-reversal symmetry gives two degenerate ground states.
Third law of thermodynamics
Some crystalline systems exhibit geometrical frustration , where the structure of the crystal lattice prevents the emergence of a unique ground state. Ground-state helium unless under pressure remains liquid. In addition, glasses and solid solutions retain large entropy at 0 K, because they are large collections of nearly degenerate states, in which they become trapped out of equilibrium. Another example of a solid with many nearly-degenerate ground states, trapped out of equilibrium, is ice Ih , which has "proton disorder".
For the entropy at absolute zero to be zero, the magnetic moments of a perfectly ordered crystal must themselves be perfectly ordered; from an entropic perspective, this can be considered to be part of the definition of a "perfect crystal". Only ferromagnetic , antiferromagnetic , and diamagnetic materials can satisfy this condition. However, ferromagnetic materials do not, in fact, have zero entropy at zero temperature, because the spins of the unpaired electrons are all aligned and this gives a ground-state spin degeneracy.
Materials that remain paramagnetic at 0 K, by contrast, may have many nearly-degenerate ground states for example, in a spin glass , or may retain dynamic disorder a quantum spin liquid. Suppose that the temperature of a substance can be reduced in an isentropic process by changing the parameter X from X 2 to X 1. One can think of a multistage nuclear demagnetization setup where a magnetic field is switched on and off in a controlled way. The process is illustrated in Fig. A non-quantitative description of his third law that Nernst gave at the very beginning was simply that the specific heat can always be made zero by cooling the material down far enough.
So the heat capacity must go to zero at absolute zero. The same argument shows that it cannot be bounded below by a positive constant, even if we drop the power-law assumption. But clearly a constant heat capacity does not satisfy Eq. That is, a gas with a constant heat capacity all the way to absolute zero violates the third law of thermodynamics.
We can verify this more fundamentally by substituting C V in Eq. The conflict is resolved as follows: At a certain temperature the quantum nature of matter starts to dominate the behavior. In both cases the heat capacity at low temperatures is no longer temperature independent, even for ideal gases. The specific heats given by Eq. Even within a purely classical setting, the density of a classical ideal gas at fixed particle number becomes arbitrarily high as T goes to zero, so the interparticle spacing goes to zero. Their heat of evaporation has a limiting value given by. If we consider a container, partly filled with liquid and partly gas, the entropy of the liquid—gas mixture is.
Nature solves this paradox as follows: