Speaker
Description
The unattainability principle of the third law of thermodynamics states that it is impossible to bring a system to its ground state within a finite number of steps. This no-go principle has been rigorously proven in a general setup, and several bounds on the achievable error in terms of reservoir parameters have been derived in the literature. However, the quantitative relationship between the error and crucial resources, such as time and energetic cost, remains elusive. Moreover, there is a strong desire to generalize and quantify this principle as a unifying characteristic across diverse thermodynamic operations beyond the task of cooling.
In this talk, we present a resolution to the above problem. To this end, we introduce the concept of "separated states," where all states are classified into two distinct categories: desired states and undesired states. This notion not only encompasses the traditional third law but also significantly broadens its applicability to a wide range of thermodynamic processes, including information erasure, copying, and biological processes such as proofreading. Within a general setup, we derive a three-way trade-off relation that connects the operational time, energetic cost, and attainable error associated with achieving separated states. This relation rigorously quantifies the principle that as thermodynamic operations approach absolute precision, they inevitably require either infinite operation time or infinite thermodynamic cost. Our results represent a significant generalization of the unattainability principle, central to the third law, and offer a fresh perspective on thermodynamic limitations. Lastly, we address several open questions in this direction.
