Abstract
The time-dependent entropy of a single free quantum particle in the non-relativistic regime is studied in detail for the process started from a fully coherent quantum state to thermodynamic equilibrium with its surroundings at a finite temperature. It is shown that the entropy at the end of the process converges to a universal constant, as a result of thermal interaction.
Highlights
It is well-known that entropy, as the measure of “the amount of uncertainty”, can not decrease in any spontaneous process according to the second law of thermodynamics [1]
The time-dependent entropy of a single free quantum particle in the non-relativistic regime is studied in detail for the process started from a fully coherent quantum state to thermodynamic equilibrium with its surroundings at a finite temperature
It is shown that the entropy at the end of the process converges to a universal constant, as a result of thermal interaction
Summary
It is well-known that entropy, as the measure of “the amount of uncertainty”, can not decrease in any spontaneous process according to the second law of thermodynamics [1]. Taking into account the detailed configuration of diffraction in real space and thermal interaction with the surround space at a finite temperature, the complicated behavior of the time-dependent internal energy is studied for the whole process started from a fully coherent quantum state to thermodynamic equilibrium with the surrounding space. The purpose of the present article is to present the detailed derivation of the expression of the time-dependent entropy for the particle and study in more detail the physics in the irreversible process. The system studied here is the simplest quantum system at a finite temperature, it already shows how a single quantum particle feels the temperature of its surrounding space. Our results here confirm the conclusion that entropy is a physical observable that can be well-defined for each individual quantum system at finite temperatures [3]
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