Quantum walk, entanglement and thermodynamic laws

• Quantum entanglement between position and chirality and thermodynamic laws.
• We propose a temperature function in order to characterize this equilibrium.
• We show the first and second laws of thermodynamics to the quantum walk (QW).
• We show that the QW entropy has upper and lower bounds.

We consider a special dynamics of a quantum walk (QW) on a line. The walker, initially localized at the origin of the line with arbitrary chirality, evolves to an asymptotic stationary state. In this stationary state a measurement is performed and the state resulting from this measurement is used to start a second QW evolution to achieve a second asymptotic stationary state. In previous works, we developed the thermodynamics associated with the entanglement between the coin and position degrees of freedom in the QW. Here we study the application of the first and second laws of thermodynamics to the process between the two stationary states mentioned above. We show that: (i) the entropy change has upper and lower bounds that are obtained analytically as functions of the initial conditions. (ii) the energy change is associated to a heat-transfer process.