Uncertainty and Thermodynamics

Dilemma

The uncertainty principle of energy and the 2nd law of thermodynamics don't add up : the uncertainty principle of energy says that

$\Delta \tau \cdot \Delta E \ge \frac{h}{4\pi} = \frac{\hbar}{2}$

where $\Delta$ is the uncertainty in measurement.

Now lets consider a situation: lets say that an isolated system $A$ is in thermodynamic equilibrium. It has two particles $b$ and $c$ so that it is in the state of maximum possible entropy. To preserve the uncertainty principle, some net energy must flow from $b$ to $c$ or from $c$ to $b$, and that results in a non-equilibrium state, may be for a fraction of a fraction of a second. But the system must move from the state of maximum entropy (equilibrium) to the state of lesser entropy, which is a sure violation of the second law of thermodynamics. Does anyone have an explanation?

• your question is really hard to read and quite hard to understand. why do you claim that to preserve the uncertainty principle, some net energy must flow from b to c or from c to b [... ]? could you elaborate your reasoning further?
– seb
Apr 12, 2013 at 16:41
• Decreasing entropy for a short period does not violate the second law of thermodynamics, since the law only governs the average entropy change. Moreover with such a small number of particles, the entropy isn't really definable in a useful way - what are the macrostates for example? Apr 12, 2013 at 16:51