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In some simple cases, and at Thermodynamic Equilibrium , the results can be shown to be a consequence of the additivity property of Independent Random Variable s; namely that the Variance of the Sum is equal to the sum of the variances of the independent variables. In these cases, the physics of such systems close to the thermodynamic limit is governed by the Central Limit Theorem in Probability . For systems of large numbers of particles, the genesis of Macroscopic behavior from its Microscopic origins fades from view. For example, the Pressure exerted by a Fluid ( Gas or Liquid ) is the collective result of collisions between rapidly moving Molecule s and the walls of a container, and Fluctuates on a microscopic Temporal and Spatial Scale . Yet the pressure does not change noticeably on an ordinary macroscopic scale because these variations Average out. Even at the thermodynamic limit, there are still small detectable fluctuations in physical Quantities , but this has a negligible effect on most sensible Properties of a system. However, microscopic spatial Density fluctuations in a gas scatter Light (which is why the Sky is Blue ). These fluctuations become quite large near the Critical Point in a Gas / Liquid Phase Diagram . In electronics, Shot Noise and Johnson-Nyquist Noise can be Measured . Certain Quantum Mechanical Phenomena near the Absolute Zero of Temperature ''T'' = 0 present Anomalies ; e.g., Bose-Einstein Condensation , Superconductivity and Superfluidity . It is at the thermodynamic limit that the additivity property of macroscopic ''extensive'' Variables is obeyed. That is, the entropy of two systems or objects taken together (in addition to their Energy and Volume ) is the sum of the two separate Values . |
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