Equilibrium under flow

Abstract

Using information theory we derive a thermodynamics for systems evolving under a collective motion, i.e. under a time-odd constraint. An illustration within the Lattice gas Model is given for two model cases: a collision between two complex particles leading to a incomplete relaxation of the incoming momentum, and a self-similar expansion. A semi-quantitative connection with the determination of thermodynamical quantities in multifragmentation reactions is done showing that they are affected in a sizeable way only when the flow dominates the global energetic.PACS numbers: 64.10.+h, 25.75.Ld, 25.70.Pq Heavy ion collisions represent a unique opportunity to probe the interdisciplinary field of phase transitions in mesoscopic systems for which a non standard thermodynamics giving rise to negative heat capacities is predicted [1]. An indication of negative heat capacities has been experimentally found [2] in multifragmentation reactions. These results can be considered as a first step towards a quantitative determination of the nuclear phase diagram. Negative heat capacities have also been observed in simulations of self-gravitating systems [3] and in the melting and boiling of clusters [4].An important conceptual problem linked with multifragmentation experiments is that the outcomes of a nuclear collision are not confined in an external container but dynamically deexcite in the vacuum. In the absence of boundary conditions, collective flows can be present at the fragmentation time. Because of this time odd component, one may doubt about the applicability of equilibrium concepts. However, we will show that information theory allows a thermodynamically consistent description of open finite systems in evolution under a collective flow. We will apply this formalism to the Lattice Gas Model [5] for the particular cases of a memory of the entrance channel (transparency) and radial expansion. In both cases the properties of the system appear to be affected in a sizeable way when flow dominates the global energetics.In the Gibbs formulation of statistical mechanics an equilibrium is defined as a collection of different microstates all corresponding to the same macrostate (or statistical ensemble) defined through the average value of (a collection of) collective variables. A practical realization of a Gibbs ensemble is given by the collection of different snapshots of an isolated ergodic system evolving in time, provided that the observation time is much longer than a typical equilibration time . This type of statistical ensemble is not very useful for short-lived open systems as the transient excited states formed in a nuclear collisions. However, ergodicity is not the unique way to produce a Gibbs ensemble . Indeed, within information theory, an equilibrium corresponds to any ensemble of states that maximizes the entropy in a given space under the constraint of (a number of) observables known in average [9]. Therefore, if the nuclear dynamics is sufficiently sensitive to the initial conditions, the ensemble of outcomes...

Thermodynamics of Fluids Under Flow

“…Gulminelli (2004) and Gulminelli and Chomaz (2004) have used information theory to derive a thermodynamics for systems in the presence of a collective flow, introducing information on such a flow by means of suitable Lagrange multipliers, as it has been illustrated in Sect. Gulminelli (2004) and Gulminelli and Chomaz (2004) have used information theory to derive a thermodynamics for systems in the presence of a collective flow, introducing information on such a flow by means of suitable Lagrange multipliers, as it has been illustrated in Sect.…”

Statistical analysis of a dynamical multifragmentation path

“…However, the comparison process is complicated by the presence of several effects, such as pre-equilibrium particle emission, collective radial expansion (see, e.g., Ref. [6]), Coulomb propagation of the breakup primary fragments, and secondary particle emissions. So it is difficult to ascertain whether these quantities really correspond to the source properties obtained at a given time during the fragmentation path.…”