Thermodynamic Anomalies of Small Quantum Systems Within a New Approach to Statistical Physics

Abstract

Based on a new statistical theory, we investigate the thermodynamic anomalies of small quantum systems, such as the negative specific heat (NSH) and negative entropy (NE) within the generalized canonical ensemble. We consider the systembath heat exchange and "uncompensated heat" in the thermodynamical level which is independent on the details of the system-bath coupling. For ideal finite systems, we calculate two thermodynamic quantities, i.e., the experimental specific heat and the entropy. The results show that the NSH and NE exist in quantum thermodynamics, particularly at low temperatures for small systems. They agree with the results of the reduced partition function theory and reveal that the finite boundary effects of the uncompensated heat and heat exchange of small quantum systems dominate the nonequilibrium irreversible processes. Keywords Small quantum system · Negative specific heat · Negative entropy Thermodynamics and the traditional statistical-mechanical interpretation are originally developed for large systems in the equilibrium state. However, the theories are not sufficient to describe the thermodynamical properties of small quantum systems [1-3]. There are increasing findings of anomalies presented experimentally in these systems [4][5][6][7][8][9]. These experimental results [6,10,11] turn up the existence of negative specific heat (NSH) and negative entropy (NE) [12]. But the specific heat is necessarily positive both in the standard Boltzmann-Gibbs statistical theories of the canonical ensemble (CE) and grand-canonical ensemble (GCE) and in the exact CE theory on the

Stochastic and Macroscopic Thermodynamics of Strongly Coupled Systems

“…Others have argued that the validity of the second law is restored by accounting for the heat associated with coupling the system to its reservoir [35,73,74] or by introducing an effective equilibrium temperature [75]. Additional subtleties arise in the evaluation of specific heat for a quantum system strongly coupled to a bath of harmonic oscillators [76][77][78][79].…”