Universal Landauer-like inequality from the first law of thermodynamics

We demonstrate that the equality-based first law of thermodynamics inherently implies a universal Landauer -like inequality, connecting variations in system entropy and energy. This Landauer-like inequality is shown to depend solely on system information and is highly applicable in scenarios where the implementation of the conventional Landauer principle becomes challenging. Moreover, we unveil that this Landauer-like inequality complements the Landauer principle by establishing an alternative upper bound on heat dissipation. To un-derscore its practicality, we illustrate the utility of the Landauer-like inequality in contexts such as dissipative quantum state preparation and quantum information erasure applications. Our findings offer insights into iden-tifying thermodynamic constraints, with particular relevance to the domains of quantum thermodynamics and the energetics of quantum information processing. Additionally, this approach paves the way for investigating systems coupled to nonthermal baths or those characterized by limited access to bath information.