Thermostat with a local heat-bath coupling for exact energy conservation in dissipative particle dynamics

We present a Markov process which models particle hydrodynamics with conservation of the first three momenta. This is achieved by extending the [Peters, Europhys. Lett. 66, 311 (2004)] and [Lowe, Europhys. Lett. 47, 145 (1999)] method to incorporate energy conservation. The equivalence of the energy conserving Peters method and dissipative particle dynamics with energy conservation (DPDE) in the limit of a vanishing time step is shown. Simple numerical experiments clearly demonstrate the applicability of the methods. This overcomes current limitations of DPDE in the study of complex fluids in the (N,V,E) ensemble.