A proposal for the thermodynamics of certain open systems

Abstract

Motivated by the fact that the (inverse) temperature might be a function of the energy levels in the Planck distribution $n_{\epsilon }=\frac{1}{{\zeta }^{-1}{e}^{\beta (\epsilon )\epsilon }-1}$ for the occupation number $n_{\epsilon }$ of the level $\epsilon$, we show that it can be naturally achieved by imposing the constraint concerning the conservation of a weighted sum ${\sum }_{\epsilon }f(\epsilon )\epsilon n_{\epsilon }$, with a fixed positive weight function $f$, of the contributions of the single energy levels occupation in the Microcanonical Ensemble scheme, obtaining $\beta (\epsilon )\propto f(\epsilon )$. This immediately addresses the possibility that also a weighted sum ${\sum }_{\epsilon }g(\epsilon )n_{\epsilon }$ of the particles occupation number is conserved, having as a consequence that the chemical potential might be a function of the energy levels of the system as well. This scheme leads to a thermodynamics of open systems in the following way: the equilibrium is reached when the entropy function is maximised under the constraints that some weighed sums of occupation of the energy levels and the occupation numbers are conserved. The standard case of isolated systems corresponds to the weight functions being trivial (i.e. $f,g$ are identically 1). For such open systems, new and unexpected phenomena which might happen in nature can appear, like the Bose Einstein Condensation in excited levels. The ideas outlined in the present paper may provide a new approach for the treatment of the irreversible thermodynamics.

arXiv comment20 pages, to appear in Physica A

References in corpus (9)

• Bose-Einstein condensation of photons in an optical microcavity
• Schwinger-Keldysh theory for Bose-Einstein condensation of photons in a dye-filled optical microcavity
• First law of thermodynamics for dynamical apparent horizons and the entropy of Friedmann universes
• Harmonic analysis on inhomogeneous amenable networks and the Bose--Einstein condensation
• Bose Einstein condensation on inhomogeneous amenable graphs
• Bekenstein-Hawking entropy in expanding universes from black hole theorems
• Bose-Einstein condensation and condensation of $q$-particles in equilibrium and non equilibrium thermodynamics: a new approach
• Entropy, energy and temperature-length inequality for Friedmann universes
• A statistical representation of the cosmological constant from finite size effects at the apparent horizon

Cited by in corpus (6)

• Balance between quantum Markov semigroups
• Entropy, temperature and internal energy of trapped gravitons and corrections to the Black Hole entropy
• The spectrum of the Schrödinger Hamiltonian for trapped particles in a cylinder with a topological defect perturbed by two attractive delta interactions
• On the Thermodynamics of the q-Particles
• Spectral actions for q-particles and their asymptotics
• On the Thermodynamics of Particles Obeying Monotone Statistics