Abstract
We study nonequilibrium steady states of a one-dimensional stochastic model, originally introduced as an approximation of the discrete nonlinear Schrödinger equation. This model is characterized by two conserved quantities, namely mass and energy; it displays a ‘normal’, homogeneous phase, separated by a condensed (negative-temperature) phase, where a macroscopic fraction of energy is localized on a single lattice site. When steadily maintained out of equilibrium by external reservoirs, the system exhibits coupled transport herein studied within the framework of linear response theory. We find that the Onsager coefficients satisfy an exact scaling relationship, which allows reducing their dependence on the thermodynamic variables to that on the energy density for unitary mass density. We also determine the structure of the nonequilibrium steady states in proximity of the critical line, proving the existence of paths which partially enter the condensed region. This phenomenon is a consequence of the Joule effect: the temperature increase induced by the mass current is so strong as to drive the system to negative temperatures. Finally, since the model attains a diverging temperature at finite energy, in such a limit the energy–mass conversion efficiency reaches the ideal Carnot value.
Original language | English |
---|---|
Article number | 063020 |
Number of pages | 19 |
Journal | New Journal of Physics |
Volume | 25 |
Issue number | 6 |
Early online date | 22 Jun 2023 |
DOIs | |
Publication status | Published - 22 Jun 2023 |
Bibliographical note
AcknowledgmentWe thank S Lepri for many useful suggestions on coupled-transport phenomena and related models. We are also indebted to P C Semenzara for enlightening discussions on Monte Carlo methods. P P acknowledges support from the MIUR PRIN 2017 Project 201798CZLJ.
Data Availability Statement
Data availability statementThe data that support the findings of this study are available upon reasonable request from the authors.
Keywords
- transport processes (theory)
- Onsager coefficients
- real-space condensation