THERMAL INFORMATION-ENTROPIC UNCERTAINTY RELATION

Within the framework of thermo-field-dynamics, we define the reduced probability densities, and investigate the sum of information-theoretic 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 finite-temperature variational technique for the reduced system, and show that this relation, termed the thermal information-entropic 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. © 1990 The American Physical Society.