Regular Article – Quantum Optics
Potential role of uncertainty relation for thermodynamic quantities in the Planck’s cavity radiation
Muroran Institute of Technology, 27-1 Mizumoto-cho, 050-8585, Muroran, Hokkaido, Japan
Accepted: 12 July 2021
Published online: 2 August 2021
The electromagnetic field is well described in terms of one-dimensional quantum harmonic oscillator. The uncertainty product of canonically conjugate variables is quantized just like as for the energy quantization except constant factor. This is a characteristic property of the harmonic oscillator model. The thermodynamic quantities reflect the energy structure under consideration. In the same way, we can take the magnitude of uncertainty product into the thermodynamic quantities. The purpose of this paper is to study a connection between the uncertainty relation and the macroscopic thermodynamic quantities in the Planck cavity radiation. For this connection, thermal average of uncertainty product will be introduced, which is an extension of uncertainty relation to finite temperature. The spectral densities of internal energy, heat capacity, Helmholtz free energy, and entropy can be expressed by using the thermal average of uncertainty product. The quantization of uncertainty product implies physically complementarity or hidden stability between conjugate variables. It is realized that this complementarity is embedded into the individual macroscopic thermodynamic quantities. Moreover, on the fluctuation analysis, the properties of wave–particle duality are examined in graphical visualizations.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2021