Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Nov;74(5):051121. doi: 10.1103/PhysRevE.74.051121. Epub 2006 Nov 27.
Physical review. E, Statistical, nonlinear, and soft matter physics
Steffen Trimper
PMID: 17279891 DOI: 10.1103/PhysRevE.74.051121
A simple spin-flip process is analyzed under the presence of two heat reservoirs. While one flip process is triggered by a bath at temperature T, the inverse process is activated by a bath at a different temperature T'. The situation can be described by using a master equation approach in a second quantized Hamiltonian formulation. The stationary solution leads to a generalized Fermi-Dirac distribution with an effective temperature Te. Likewise the relaxation time is given in terms of Te. Introducing a spin representation we perform a Landau expansion for the averaged spin as order parameter and consequently, a free energy functional can be derived. Owing to the two reservoirs the model is invariant with respect to a simultaneous change sigma<-->-sigma and T<-->T'. This symmetry generates a third order term in the free energy which gives rise a dynamically induced first order transition.
