Fluctuations and Brownian Motion

Abstract

In thermodynamics the difference in entropy of two states I and II is given by

$${S_{II}} - {S_I} = {\left( {\int\limits_I^{II} {\frac{{\delta Q}}{T}} } \right)_{rev}}$$

((73.1))

where δQ is the heat supplied. The index “rev” means that the transition from I to II has to be carried out in a reversible way. If the quantum mechanical ground state E ₀ of the system is nondegenerate, the quantum theoretical phase volume Φ(E) approaches 1 for E just above E ₀, which means that the entropy, S & klnΦ, approaches zero. The entropy of the ground state can then be normalized to zero and one can define an absolute value of S by starting from the ground state E ₀ or from $T = 0\left( {{S_1} = {S_{{E_o}}} = 0} \right)$:

$${S_{II}} = \int\limits_I^{II} {\frac{{\delta Q}}{T}} $$

((73.1a))

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