Quantum thermodynamic

Quantum thermodynamics is the study of the relations between two independent physical theories: thermodynamics and quantum mechanics. The two independent theories address the physical phenomena of light and matter. In 1905 Einstein argued that the requirement of consistency between thermodynamics and electromagnetism...:. leads to the conclusion that light is quantized obtaining the relation ${\displaystyle E=h\nu }$. This paper is the dawn of quantum theory. In a few decades quantum theory became established with an independent set of rules. Currently quantum thermodynamics addresses the emergence of thermodynamic laws from quantum mechanics. It differs from quantum statistical mechanics in the emphasis on dynamical processes out of equilibrium. In addition there is a quest for the theory to be relevant for a single individual quantum system.

There is an intimate connection of quantum thermodynamics with the theory of open quantum systems. Quantum mechanics inserts dynamics into thermodynamics, giving a sound foundation to finite-time-thermodynamics. The main assumption is that the entire world is a large closed system, and therefore, time evolution is governed by a unitary transformation generated by a global Hamiltonian. For the combined system bath scenario, the global Hamiltonian can be decomposed into:

where ${\displaystyle H_{S}}$ is the system’s Hamiltonian, ${\displaystyle H_{B}}$ is the bath Hamiltonian and ${\displaystyle H_{SB}}$ is the system-bath interaction. The state of the system is obtained from a partial trace over the combined system and bath: ${\displaystyle \rho _{S}(t)=Tr_{B}(\rho _{SB}(t))}$. Reduced dynamics is an equivalent description of the systems dynamics utilizing only systems operators. Assuming Markov property for the dynamics the basic equation of motion for an open quantum system is the Lindblad equation(L-GKS):

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