On the entropy operator for the general SU(1,1) TFD formulation

TL;DR

This paper introduces an entropy operator within the SU(1,1) Thermo Field Dynamics framework, applied to a bosonic string, to derive thermal states and analyze their properties at finite temperature.

Contribution

It proposes a new entropy operator for the SU(1,1) TFD formulation and applies it to construct thermal states of a bosonic string.

Findings

Thermal vacuum constructed for the bosonic string.

Thermal effects unaffected by breve conjugation.

Derived thermal energy, entropy, and free energy for the system.

Abstract

In this letter, an entropy operator for the general unitary SU(1,1) TFD formulation is proposed and used to lead a bosonic system from zero to finite temperature. Namely, considering the closed bosonic string as the target system, the entropy operator is used to construct the thermal vacuum. The behaviour of such a state under the breve conjugation rules is analized and it was shown that the breve conjugation does not affect thermal effects. From this thermal vacuum the thermal energy, the entropy and the free energy of the closed bosonic string are calculated and the apropriated thermal distribution for the system is found after the free energy minimization.