**Olivier Dauchot
**

**INTENSIVE THERMODYNAMIC PARAMETERS IN STATIONARY NON
EQUILIBRIUM SYSTEMS
**

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.