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The thermodynamic limit is essentially a consequence of the central limit theorem of probability theory. The internal energy of a gas of N molecules is the sum of order N contributions, each of which is approximately independent, and so the central limit theorem predicts that the ratio of the size of the fluctuations to the mean is of order 1/N 1/2.
This refinement is sometimes called the Landauer bound, or Landauer limit. In 2008 and 2009, researchers showed that Landauer's principle can be derived from the second law of thermodynamics and the entropy change associated with information gain, developing the thermodynamics of quantum and classical feedback-controlled systems. [6] [7]
Thermodynamic efficiency limit is the absolute maximum theoretically possible conversion efficiency of sunlight to electricity. Its value is about 86%, which is the Chambadal-Novikov efficiency , an approximation related to the Carnot limit , based on the temperature of the photons emitted by the Sun's surface.
By contrast, in the thermodynamic limit, () may exhibit a non-analytic behavior. Using that Z ( q ) {\displaystyle Z(q)} is an entire function for finite system sizes, Lee–Yang theory takes advantage of the fact that the partition function can be fully characterized by its zeros in the complex plane of q {\displaystyle q} .
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The Shockley–Queisser limit, zoomed in near the region of peak efficiency. In a traditional solid-state semiconductor such as silicon, a solar cell is made from two doped crystals, one an n-type semiconductor, which has extra free electrons, and the other a p-type semiconductor, which is lacking free electrons, referred to as "holes."
Due to the other causes detailed below, practical engines have efficiencies far below the Carnot limit. For example, the average automobile engine is less than 35% efficient. Carnot's theorem applies to thermodynamic cycles, where thermal energy is converted to mechanical work.
However, in the thermodynamic limit (i.e. in the limit of infinitely large system size), the specific entropy (entropy per unit volume or per unit mass) does not depend on . The entropy is thus a measure of the uncertainty about exactly which quantum state the system is in, given that we know its energy to be in some interval of size δ E ...