Journal of Research on Many-body Systems

Journal of Research on Many-body Systems

Inequalities for quantum thermodynamics in infinite space

Document Type : Full length research Paper

Authors
farzollah Mirzapour 1
Reza Rasuli 2
1 Department of mathematics, University of Zanjan, Iran
2 Department of physics, University of Zanjan
10.22055/jrmbs.2021.16568
Abstract
In statistical mechanics, the upper limit of entropy is very important for determining the final state of the system based on the Helmholtz variational principle. Hence many attempts have been made to calculate the entropy of the system, and a thermodynamic theory based on Renyi entropy has recently been presented that can describe new states in the thermodynamic system. The exact determination of entropy can not be done in many cases, and therefore approximate methods are used. An approximate solution often involves obtaining a high limit for entropy, which determines the final state of the system. This paper presents an upper limit for quantum entropy. For this purpose, the calculations are carried out in a separable Hilbert space with orthogonal bases. Using the Shanon definition of entropy, the upper limit is calculated for the relative entropy of two commutative operators.
Keywords
Relative entropy
Hilbert space
thermodynamic inequality
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  • Receive Date 29 October 2019
  • Revise Date 13 October 2020
  • Accept Date 30 January 2021