Abstract
We develop the full counting statistics of dissipated heat to explore the relation with Landauer’s principle. Combining the two-time measurement protocol for the reconstruction of the statistics of heat with the minimal set of assumptions for Landauer’s principle to hold, we derive a general one-parameter family of upper and lower bounds on the mean dissipated heat from a system to its environment. Furthermore, we establish a connection with the degree of non-unitality of the system’s dynamics and show that, if a large deviation function exists as stationary limit of the above cumulant generating function, then our family of lower and upper bounds can be used to witness and understand first-order dynamical phase transitions. For the purpose of demonstration, we apply these bounds to an externally pumped three level system coupled to a finite sized thermal environment.
Highlights
In his landmark 1961 paper, Rolf Landauer demonstrated that the heat dissipated in an irreversible computational process must always be at least equal to the corresponding information theoretic entropy change [1]
We show how the bounds relate to a large deviation function (LDF), which is typically used for analyzing the long time statistical properties of a given system [37]
We have presented a method to derive a one-parameter family of Landauer-like bounds for the mean dissipated heat based on the two-time measurement protocol
Summary
We develop the full counting statistics of dissipated heat to explore the relation with Landauer’s principle. Combining the two-time measurement protocol for the reconstruction of the statistics of heat with the minimal set of assumptions for Landauer’s principle to hold, we derive a general oneparameter family of upper and lower bounds on the mean dissipated heat from a system to its environment. We establish a connection with the degree of non-unitality of the system’s dynamics and show that, if a large deviation function exists as stationary limit of the above cumulant generating function, our family of lower and upper bounds can be used to witness and understand first-order dynamical phase transitions. For the purpose of demonstration, we apply these bounds to an externally pumped three level system coupled to a finite sized thermal environment
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