The thermodynamic entropy of a macroscopic quantum system is a continuous function of energy

Abstract

The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper, I analyze and calculate the thermodynamic entropy for large, but finite quantum mechanical systems. A special feature of this analysis is that the thermodynamic energy of a quantum system is shown to be a continuous variable, rather than being associated with discrete energy eigenvalues. Calculations of the entropy as a function of energy can be carried out with a Legendre transform of thermodynamic potentials obtained from a canonical ensemble. The resultant expressions for the entropy are also able to describe equilibrium between quantum systems having incommensurate energy-level spacings. This definition of entropy preserves all required thermodynamic properties, including satisfaction of all postulates and laws of thermodynamics. It also demonstrates the consistency of the concept of negative temperature with the principles of thermodynamics.

References in corpus (6)

• Gibbs, Boltzmann, and negative temperatures
• Construction of microcanonical entropy on thermodynamic pillars
• System-size scaling of Boltzmann and alternate Gibbs entropies
• The Gibbs "volume" entropy is incorrect
• Comment on "Consistent thermostatistics forbids negative absolute temperatures"
• Thermodynamic laws in isolated systems

Cited by in corpus (12)

• Complete analysis of ensemble inequivalence in the Blume-Emery-Griffiths model
• In defence of negative temperature
• Entropy and the second law for driven, or quenched, thermally isolated systems
• The definition of the thermodynamic entropy in statistical mechanics
• Comparative Microscopic Study of Entropies and their Production
• Measuring energy by measuring any other observable
• A microcanonical entropy correcting finite-size effects in small systems
• Long-time equilibration can determine transient thermality
• Finite thermal reservoirs and the canonical distribution
• Resolving the debate about proposed expressions for the classical entropy
• Typical Positivity of Nonequilibrium Entropy Production for Pure States
• Generalized uncertainty relation between thermodynamic variables in quantum thermodynamics