Aditya Jha - The Anatomy of Thermal Equilibrium and Fluctuation-Dissipation Theorems

Aditya Jha (Cambridge University)

The Center for Philosophy of Science at the University of Pittsburgh invites you to join us for our Lunch Time Talk. Attend in person at 1117 Cathedral of Learning or visit our live stream on YouTube at https://www.youtube.com/channel/UCrRp47ZMXD7NXO3a9Gyh2sg.

LTT: Aditya Jha

Tuesday, October 6th @ 12:00 pm - 1:30 pm EST

Title: The Anatomy of Thermal Equilibrium and Fluctuation-Dissipation Theorems

Abstract:

Two questions are foundational to equilibrium statistical mechanics and statistical thermodynamics: what justifies taking the Gibbs state to be the state of thermal equilibrium, and what justifies a system’s approach to that state. Much of the literature focuses on the second question, and on the debates around typicality, ergodicity and entropy increase that have historically accompanied it. I show that focusing on the first is rewarding in its own right, and accordingly argue for three claims. Firstly, a satisfactory answer to the first question can be given on operational (thermodynamic) grounds alone, something the physics literature recognized only much later than Gibbs did: the passivity theorems of Pusz and Woronowicz (1978) and Lenard (1978), and related recent accounts, overlook the arguments to this effect already in Gibbs (1902), as well as those in Szilard (1925). Secondly, such an answer reveals the precise structure of the state of thermal equilibrium, which is more than the mere stationarity of an ensemble; it is the conjunction of three conditions: stationarity, detailed balance, and a compositional (operational) condition on energies and probabilities that forces probability to be logarithmically linear in energy. Thirdly, this precise structure is what has unified thermal physics to a significant degree, both historically and in the contemporary literature, though without due recognition as such. The structure is employed by some fluctuation-dissipation theorems, from Einstein through Nyquist to Callen and Welton, and partly by the modern generalized fluctuation theorems such as the Jarzynski equality. It also underlies the contemporary and more general characterization of thermal equilibrium as KMS states (Haag et al. 1967), where the analytic condition on correlation functions encodes just this detailed balance.

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