Work and heat at strong coupling
For a stated strong-coupling experiment, specify accessible energy measurements, work storage and interaction-energy accounting, then derive testable work/heat statistics and fluctuation relations with controlled effects of initial correlations and measurement
Problem statement
For a stated strong-coupling experiment, specify accessible energy measurements, work storage and interaction-energy accounting, then derive testable work/heat statistics and fluctuation relations with controlled effects of initial correlations and measurement disturbance.
Lean 4
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Background
Even in ordinary thermodynamics work and heat depend on an operational partition and protocol. At strong system–bath coupling the interaction energy cannot be neglected, and initial correlations and quantum energy-measurement disturbance make those choices particularly important. Different valid bookkeeping schemes need not describe the same task.
What is known: A leading approach uses the Hamiltonian of mean force to define a system 'effective' internal energy and entropy such that equilibrium thermodynamic relations are preserved (Seifert; Talkner–Hänggi); this yields a consistent equilibrium thermodynamics at strong coupling. For nonequilibrium processes, various definitions of work and heat (based on the two-point measurement scheme, on the bath energy change, or on the system+interaction) disagree, and fluctuation theorems can be formulated but depend on the chosen split. Reaction-coordinate and HEOM methods (O3) give numerically consistent accounts in specific models.
A published no-go theorem of Perarnau-Llobet et al. shows that, for coherent closed-system protocols, a positive work-measurement scheme cannot in general both reproduce the average energy change and agree with the two-point measurement distribution on incoherent states. This already rules out some demands for a unique universal definition; it does not forbid model-specific operational thermodynamics.
The frontier is a stated experiment: compare battery work, calorimetric heat and interaction-energy accounting; prove which fluctuation relation survives the chosen preparation and measurement procedure, and bound corrections or inaccessible contributions. Agreement on one convention is not the success criterion. Related: O3, O6, O7.
Progress & source assessment
Source catalogue review: 4 September 2026. Improved indicates partial progress, including qualified preprint claims.
- [1]Talkner & Hänggi, 'Colloquium: Statistical mechanics and thermodynamics at strong coupling', Rev. Mod. Phys. 92, 041002 (2020) link
- [2]Seifert, 'First and second law of thermodynamics at strong coupling', PRL 116, 020601 (2016) link
- [3]Perarnau-Llobet et al., 'No-go theorem for the characterization of work fluctuations in coherent quantum systems', PRL 118, 070601 (2017) link
Recorded progress
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