Quantum mechanics and the nature of the second law of thermodynamics

Barbara Drossel

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.

Shoichi Nagata

Boltzmann’s statistical interpretation of the second law of thermodynamics indicates that systems evolve from less probable to more probable states. In an isolated system, entropy reaches its maximum at equilibrium, corresponding to the greatest number of accessible microstates. The quantum uncertainty principle, a fundamental feature of quantum mechanics, reflects the intrinsic probabilistic nature of physical systems. This study proposes that the equilibrium state defined by maximal entropy and microstate accessibility also represents a condition of maximal intrinsic uncertainty. We examine the connection between Boltzmann’s entropy framework and the quantum mechanical uncertainty relation between position and momentum, focusing on localized harmonic oscillator systems. Properties of the uncertainty product are analyzed in detail. Both the uncertainty principle and the second law of thermodynamics are rooted in probabilistic foundations. Our findings suggest that the uncertainty principle provides a conceptual perspective on thermodynamic behavior.

Ping-Xing, Chen, Jianming +5 more

Jonathan Oppenheim

Akira Suzuki, Hisao Taira

We propose a representation of the basic laws, namely the zeroth, first, second and third law, in quantum thermodynamics. The zeroth law is represented by some parameters () that specify respective quantum states. The parameters are the elements of thermodynamic state space. The introduction of such parameters is based on a probabilistic nature of quantum theory. A quantum analog of the first law can be established by utilizing these parameters. The notion of heat in quantum systems is clarified from the probabilistic point of view in quantum theory. The representation of the second law can be naturally described in terms of these parameters introduced for the respective quantum systems. In obtaining the representation of quantum thermodynamics, consistency between quantum theory and classical thermodynamics should have been preserved throughout our formulation of quantum thermodynamics. After establishing the representation of the second law, the third law is discussed briefly. The relationship between thermodynamic temperatures and the parameters in is also discussed.