Quantum Boltzmann Law

Yves Pomeau A, Minh-Binh Tran

Qian Du, Kui Cao, Su-Peng Kou

We study parity-time-symmetric non-Hermitian quantum systems at finite temperature, where the Boltzmann distribution law fails to hold. To characterize their abnormal physical properties, a quantum statistical theory (the so-called quantum Liouvillian statistical theory) is developed, in which the Boltzmann distribution law is replaced by the Liouvillian-Boltzmann distribution law. Using the theory, we derive analytical results of thermodynamic properties for parity-time-symmetric non-Hermitian quantum systems and find that a ``continuous'' thermodynamic phase transition occurs at the exceptional point, where a zero-temperature anomaly exists.

Tolga Yarman, Alexander L. Kholmetskii, Ozan Yarman +2 more

We show that the second law of thermodynamics is rooted in quantum mechanics, inasmuch as allowing the substitution of the Boltzmann constant k and temperature with respectively the Planck constant and quantum numbers. In particular, we will see that the entropy S becomes proportional to the natural logarithm of the average of the squared quantum numbers n2‾, where each quantum number is associated with a quantum state of the constituents of the thermodynamical system under consideration. It is important to stress that the present approach furnishes the corrected Boltzmann entropy expression. Thus, instead of S=klnΩ, with Ω in the former signifying the number of Boltzmann microstates, we land at S=klnn2‾ The results obtained are discussed.

Bassano Vacchini, Klaus Hornberger

László Erdős, Manfred Salmhofer B, Horng‐Tzer Yau

F. Borgonovi, Felix M. Izrailev

We study the emergence of Boltzmann's law for the "single-particle energy distribution" in a closed system of interacting classical spins. It is shown that for a large number of particles Boltzmann's law may occur, even if the interaction is very strong. Specific attention is paid to classical analogs of the average shape of quantum eigenstates and "local density of states," which are very important in quantum chaology. Analytical predictions are then compared with numerical data.