Thermodynamic analysis of algorithmic cooling protocols: Efficiency metrics and improved designs

Algorithmic cooling (AC) protocols have been predominantly studied for their cooling capabilities, with limited attention paid to their thermodynamic properties. This work explores an alternative perspective by analyzing a broad family of AC protocols from a thermodynamic standpoint. First, we give an in-depth review and formal classification of standard AC protocols. Leveraging the transfer matrix formalism, we achieve a consistent calculation of performance metrics, encompassing both cooling limits and target state evolution. We obtained a unification of these diverse cooling limits into a single, coherent mathematical expression, streamlining comparative analyses. Then, to assess the efficiency of coherent cooling protocols, we introduce two generic metrics: the coefficient of performance $K$ and Landauer's Ratio $R_L$, and establish a direct interrelation. Applying these metrics, we thoroughly evaluate selected AC protocols, highlighting their relative strengths. Finally, we propose improved versions of AC protocols that exhibit enhanced thermodynamic performance, achieving desired target temperatures with lower work inputs. This research contributes to a deeper understanding of AC protocols and provides valuable insights for designing efficient cooling strategies in various applications.