Joint Fluctuation Theorems for Sequential Heat Exchange

• Main Authors: Jader Santos, André Timpanaro, Gabriel Landi
• Format: Article
• Language: English
• Published: MDPI AG 2020-07-01
• Series: Entropy
• Subjects: fluctuation theorems; collisional models
• Online Access: https://www.mdpi.com/1099-4300/22/7/763

We study the statistics of heat exchange of a quantum system that collides sequentially with an arbitrary number of ancillas. This can describe, for instance, an accelerated particle going through a bubble chamber. Unlike other approaches in the literature, our focus is on the <i>joint</i> probability distribution that heat <inline-formula> <math display="inline"> <semantics> <msub> <mi>Q</mi> <mn>1</mn> </msub> </semantics> </math> </inline-formula> is exchanged with ancilla 1, heat <inline-formula> <math display="inline"> <semantics> <msub> <mi>Q</mi> <mn>2</mn> </msub> </semantics> </math> </inline-formula> is exchanged with ancilla 2, and so on. This allows us to address questions concerning the correlations between the collisional events. For instance, if in a given realization a large amount of heat is exchanged with the first ancilla, then there is a natural tendency for the second exchange to be smaller. The joint distribution is found to satisfy a Fluctuation theorem of the Jarzynski–Wójcik type. Rather surprisingly, this fluctuation theorem links the statistics of multiple collisions with that of independent single collisions, even though the heat exchanges are statistically correlated.