  We propose an experiment to investigate the possibility of long-distance
thermodynamic relationships between two entangled particles. We consider a pair
of spin 1/2 particles prepared in an entangled singlet state in which one
particle is sent to Alice and the other to her distant mate Bob, who are
spatially separated. Our proposed experiment consists of three different
setups: First, both particles are coupled to two heat baths with various
temperatures. In the second setup, only Alice's particle is coupled to a heat
bath and finally, in the last setup, only Bob's particle is coupled to a heat
bath. We study the evolution of an open quantum system using the first law of
thermodynamics based on the concepts of ergotropy, adiabatic work, and
operational heat, in a quantum fashion. We analyze and compare ergotropy and
heat transfer in three setups. Our results show that the heat transfer for each
entangled particle is not independent of the thermalization process that occurs
for the other one. We prove that the existence of quantum correlations affects
the thermodynamic behavior of distant particles in an entangled state.
