INTENSIVE THERMODYNAMIC PARAMETERS IN STATIONARY NON
Considering a broad class of steady-state non-equilibrium systems for which some additive quantities are conserved by the dynamics, we introduce from a statistical approach intensive thermodynamic parameters (ITPs) conjugated to the conserved quantities. This definition does not require any detailed balance relation to be fulfilled. Rather, the system must satisfy a general additivity property, which holds in most of the models usually considered in the literature, including those described by a matrix product ansatz with finite matrices. Note that the systems considered here are out of equilibrium not due to the presence of gradients imposed, for instance, by boundary reservoirs, but because of the breaking of micro-reversibility (that is, time-reversal invariance) at the level of the microscopic dynamics in the bulk.
The main property of these ITPs is to take equal values in two subsystems, making them a powerful tool to describe non-equilibrium phase coexistence, as illustrated on different models.
We then discuss the issue of the equalization of ITPs when two different systems are put into contact. Although the proposed generalization of ITPs appears to be rather natural, it turns out that nontrivial problems arise as soon as systems with different dynamics are put into contact. This issue is essential if one wants to measure an ITP using a small auxiliary system just like temperature is measured with a thermometer and points at one of the main difficulties of non-equilibrium statistical mechanics.
Finally, an efficient alternative determination, based on the measure of fluctuations, is also proposed and illustrated.