Large (and Small) Energy Fluctuations in a Single Classical Degree of Freedom and the Second Law of Thermodynamics
Abstract
Energy fluctuations in a single classical degree of freedom above the ground state at thermodynamic equilibrium at temperature T are typically of average magnitude ∼ k_{B}T. However, we show that the average magnitude of such fluctuations can be much larger (or much smaller) than k_{B}T, indeed, that at least in principle it can be infinite (or arbitrarily close to 0). Nevertheless, the average energy fluctuation magnitude being untypically large (or untypically small) does not violate the second law of thermodynamics. For, if the average magnitude of energy fluctuations is much larger than k_{B}T, then particle motion along the degree of freedom must manifest extreme spatial delocalization. The cost of locating the fluctuating particle along its degree of freedom equals or exceeds the large energy gain obtained upon finding it with an energy of much more than k_{B}T above its ground state. The particle loses as much or more ability to do work via its spatial delocalization than it gains via the energy fluctuation. Similarly, if the average magnitude of energy fluctuations is much smaller than k_{B}T, then the small energy yield obtainable upon locating the particle is compensated for by the small cost of locating it.
 Publication:

Second Law of Thermodynamics: Status and Challenges
 Pub Date:
 December 2011
 DOI:
 10.1063/1.3665248
 Bibcode:
 2011AIPC.1411..351D
 Keywords:

 thermodynamics;
 interface states;
 harmonic oscillators;
 potential energy functions;
 05.70.Ce;
 73.20.Jc;
 03.65.Ge;
 31.50.Bc;
 Thermodynamic functions and equations of state;
 Delocalization processes;
 Solutions of wave equations: bound states;
 Potential energy surfaces for ground electronic states