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This study presents analytical heat fluctuation theorems for transient regimes in systems coupled to heat baths. These findings generalize existing theorems for both classical and quantum systems.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Quantum Mechanics

Background:

  • Understanding heat exchange dynamics in finite systems is crucial for thermodynamics.
  • Heat fluctuation theorems provide insights into the statistical behavior of energy transfer.
  • Existing theorems often focus on equilibrium or specific transient conditions.

Purpose of the Study:

  • To derive analytical results for heat fluctuation theorems in the transient regime.
  • To investigate heat exchange statistics for systems coupled to single and multiple heat baths.
  • To extend these findings to quantum systems and compare with classical counterparts.

Main Methods:

  • Hamiltonian dynamics of composite systems (system + reservoir).
  • Derivation of heat fluctuation theorems for classical systems with external driving protocols.
  • Extension to quantum systems using von Neumann two-point projective measurements.

Main Results:

  • Analytical heat fluctuation theorems derived for the transient regime.
  • Agreement with known results for single heat bath scenarios.
  • Generalization to two heat baths and demonstration of similar relations in the quantum regime.

Conclusions:

  • The derived theorems generalize the Jarzynski-Wòjcik heat fluctuation theorem.
  • The study bridges classical and quantum thermodynamics in transient regimes.
  • The methods used for classical systems complement the analysis of quantum systems.