With the help of a general expression of the entropies in extensive and nonextensive systems, some important relations between thermodynamics and statistical mechanics are revealed through the views of thermodynamics and statistical physics. These relations are proved through the MaxEnt approach...

A new model of the energy selective electron (ESE) heat engine with a variable bias voltage resulting from a variable load resistance is established. Analytical expressions for the power output and efficiency of the system are derived, based on the Fermi–Dirac distribution of electrons. The...

A new model of micro-/nanoscaled heat engines consisting of two thin long tubes with the same length but different sizes of cross section, which are filled up with ideal quantum gases and operated between two heat reservoirs, is put forward. The working fluid of the heat engine cycle goes...

It is shown that a small system in thermodynamic equilibrium with a finite thermostat can have a q-exponential probability distribution which closely depends on the energy nonextensivity and the particle number of the thermostat. The distribution function will reduce to the exponential one at...

On the basis of Tsallis’ entropy and the joint probability factorization condition, two controversial problems existing in Tsallis’ statistics are investigated, where one is whether energy is extensive or not and the other is whether it is necessary to introduce the so-called generalized...

The spatial and momentum distributions of a weakly interacting Fermi gas trapped in a spherical symmetric power-law potential are investigated, based on the mean field approximation. The concepts of “Fermi spheres” in both the coordinate and momentum spaces are introduced and the problem of...

An analytical description on the thermodynamic properties of a weakly interacting Bose gas trapped in a power-law potential is presented, based on the local-density approximation (LDA) and the principle of the constancy of chemical potentials in equilibrium. The analytical expressions for some...

Based on the principle of maximum entropy, the q-exponential distribution can be derived from several different nonextensive entropies including the incomplete entropy. It is widely used in nonextensive statistical mechanics. In the present paper, it is shown that the incomplete expectation...

An irreversible cycle model of a solar-driven Brayton heat engine is established, in which the heat losses of the solar collector and the external and internal irreversibilities of the heat engine are taken into account, and used to investigate the optimal performance of the cycle system. The...

The performance of a quantum-mechanical heat pump using many non-interacting spin-1/2 systems as the working substance and consisting of two isothermal and two isomagnetic field processes is investigated, based on the quantum master equation and semi-group approach. The inherent regenerative...