Relativistic statistical mechanics and hydrodynamics

RECENT RESULTS

• Local thermodynamic equilibrium and four-temperature

Local thermodynamic equilibrium can be defined in relativistic quantum field theory without reference to an underlying kinetic theory. This is the implied result of the research work carried out by Zubarev, Van Weert and others in the '70s. We have reworked this problem in the context of relativistic hydrodynamics (see here) showing that it naturally leads to define a hydrodynamic frame based on the concept of local equilibrium where the velocity field is defined by the four-temperature β and not vice-versa. This frame has several important features, including that β becomes a Killing vector at global equilibrium (see here), unlike the eigenvector of the stress-energy tensor defining the so-called Landau frame.

• Thermodynamic equilibrium with acceleration and rotation

In special relativity, thermodynamic equilibrium (maximal entropy with constraints) is possible with non-vanishing acceleration and angular velocity or a combination thereof. In such a situation, because the density operator breaks some symmetries, the stress-energy tensor is no longer of the traditional "perfect fluid" form and acquires non-vanishing quantum corrections which can be determined perturbatively (see also here and here) or, for free quantum fields, can be calculated exactly. A general method to obtain the exact results resumming a divergent series was put forward in this work, were the concept of analytic distillation of a complex function was introduced. This method has been extended to fermionic case in this work.

• Unruh effect and limiting temperature

• An exact formula for entropy current

In relativity, the second law of thermodynamics must be expressed with local quantities. Thus, entropy increase becomes the positivity of the divergence of an entropy current. Can the existence of an entropy current deduced in a quantum field theoretical framework? We proved that an entropy current does exist, at local thermodynamic equilibrium, under quite general conditions in this work, and a formula to obtain it was put forward.

• Quantum relativistic fluid with longitudinal boost invariance