Can Thermodynamic Behavior of Alice’s Particle Affect Bob’s Particle?

Abstract

We propose an experiment to investigate the possibility of long-distance thermodynamic relationships between two entangled particles. We consider a pair of spin-$$\frac{1}{2}$$ 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.

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“…which is easily derived from eqn (13) considering the definition of eqn (17). The second term on the right hand side of eqn (18) involves respectively the difference between the relative entropy of coherence, the entropy of the dephased state and the logarithm of the partition function at the final and initial times of evolution and the latter arises from time variation of Hamiltonian and vanishes with time-independent Hamiltonians.…”

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“…The Lindblad master equation is of special importance because it is the most general generator of Markovian dynamics in quantum systems 36 , 37 . Here, the Lindblad master equation can be written in a generic state as follows 38 – 40 : …”

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“…The Lindblad master equation is of special importance because it is the most general generator of Markovian dynamics in quantum systems [36,37]. Here, the Lindblad master equation can be written in a generic state as follows [38][39][40]:…”