On the contribution of work or heat in exchanged energy via interaction in open bipartite quantum systems

Abstract

The question of with what we associate work and heat in a quantum thermodynamic process has been extensively discussed, mostly for systems with time-dependent Hamiltonians. In this paper, we aim to investigate the energy exchanged between two quantum systems through interaction where the Hamiltonian of the system is time-independent. An entropy-based re-definitions of heat and work are presented for these quantum thermodynamic systems therefore an entropy-based formalism of both the first and the second laws of thermodynamics are introduced. We will use the genuine reasoning based on which Clausius originally defined work and heat. The change in the energy which is accompanied by a change in the entropy is identified as heat, while any change in the energy which does not lead to a change in the entropy is known as work. It will be seen that quantum coherence does not allow all the energy exchanged between two quantum systems to be only of the heat form. Several examples will also be discussed. Finally, we will examine irreversibility from our entropy-based formalism of quantum thermodynamics.

Thermodynamics of decoherence

“…This heat dissipation is a subtle aspect of decoherence that, to our knowledge, has not yet been investigated in the literature on quantum thermodynamics. We note that several recent works have identified dissipation arising from changes in coherence, by considering the energetics of the open quantum system alone [56–58]. By contrast, by considering the full system–bath dynamics, we have shown that dissipation and pure decoherence go hand in hand even though the internal energy of the open system remains constant.…”

Thermodynamics of the Ramsey Zone

“…With these definitions, J Q(W) > 0 (J Q(W) < 0) means the two-level atom is receiving (losing) energy. Although the definition of heat and work remains a topic of discussion (see [28][29][30]), Alicki's definitions are the most widely used in the context of master equations, which is why we used them in the present study. Note that, for γ = 0 and g small enough, the dynamics is equivalent to that of an atom pumped by a classical field, being approximately unitary, and therefore, only work is associated with the atom during the evolution.…”

Two coupled spins via Ising model as the working substance for quantum Carnot and Otto cycles

“…So, the property of the working substance must be analyzed when the performance of a quantum is studied. More recently the energy exchanged between two quantum systems through interaction where the Hamiltonian of the system is timeindependent has been investigated [36].…”