A Relation Between the Second Law of Thermodynamics and Quantum Mechanics

Barbara Drossel

Ian T. Durham

You-Gang Feng Feng

We proved when random-variable fluctuations obey the central limit theorem the equality of the uncertainty relation corresponds to the thermodynamic equilibrium state. The inequality corresponds to the thermodynamic non-equilibrium state. The uncertainty relation is a quantum-mechanics expression of the second law of thermodynamics originated in wave-particle duality. Formulas of mean square-deviations changes adjusted by random fluctuations under the minimal uncertainty relation are obtained. Finally, an assumption is made which is waiting for examination. We except phase transitions in our discussion.

Sumiyoshi Abe, A. K. Rajagopal

The second law of thermodynamics in nonextensive statistical mechanics is discussed in the quantum regime. Making use of the convexity property of the generalized relative entropy associated with the Tsallis entropy indexed by q, Clausius' inequality is shown to hold in the range q in (0, 2]. This restriction on the range of the entropic index, q, is purely quantum mechanical and there exists no upper bound of q for validity of the second law in classical theory.

Ping-Xing, Chen, Jianming +5 more

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.