Thermal informationentropic uncertainty relation
Abstract
Within the framework of thermofielddynamics, we define the reduced probability densities, and investigate the sum of informationtheoretic entropies in quantum mechanics associated with the measurements of the position and momentum of a particle surrounded by the thermal environment. It is found that this quantity cannot be made arbitrarily small but has a universal lower bound dependent on the temperature. We develop the finitetemperature variational technique for the reduced system, and show that this relation, termed the thermal informationentropic uncertainty relation, is exactly saturated by the thermal coherent state. We also show that the Heisenberg uncertainty relation at finite temperature can be derived from this relation.
 Publication:

Physical Review A
 Pub Date:
 May 1990
 DOI:
 10.1103/PhysRevA.41.4608
 Bibcode:
 1990PhRvA..41.4608A
 Keywords:

 Entropy;
 Heisenberg Theory;
 Quantum Mechanics;
 Quantum Statistics;
 Heuristic Methods;
 Probability Density Functions;
 Thermodynamics and Statistical Physics;
 03.65.Bz