The general fine-grained uncertainty relation and the second law of thermodynamics

Abstract

We investigate the fine-grained uncertainty relations for qubit system by measurements corresponding respectively to two and three spin operators. Then we derive the general bound for a combination of two probabilities of projective measurements in mutually unbiased bases in $d$-dimensional Hilbert space. All of those uncertainty inequalities can be applied to construct different thermodynamic cycles such that the violation of those inequalities will lead to the violation of the second law of thermodynamics. This reveals the relationship between fine-grained uncertainty and the second law of thermodynamics.

4 pages, 1 figure

References in corpus (4)

• The Physics of Maxwell's demon and information
• The uncertainty principle determines the non-locality of quantum mechanics
• Entropic uncertainty relation for mutually unbiased bases
• Fine-grained lower limit of entropic uncertainty in the presence of quantum memory

Cited by in corpus (7)

• Entropic Uncertainty Relations and their Applications
• Majorization entropic uncertainty relations for quantum operations
• Separability conditions based on local fine-grained uncertainty relations
• Fine-grained uncertainty relation under the relativistic motion
• On entropic uncertainty relations for measurements of energy and its "complement"
• Second law of thermodynamics with quantum memory
• Rényi and Tsallis formulations of separability conditions in finite dimensions