Abstract
We study the statistics of work, dissipation, and entropy production of a quantum quasi-isothermal process, where the system remains close to the thermal equilibrium along the transformation. We derive a general analytic expression for the work distribution and the cumulant generating function. All work cumulants split into a classical (non-coherent) and quantum (coherent) term, implying that close to equilibrium there are two independent channels of dissipation at all levels of the statistics. For non-coherent or commuting protocols, only the first two cumulants survive, leading to a Gaussian distribution with its first two moments related through the classical fluctuation-dissipation relation. On the other hand, quantum coherence leads to positive skewness and excess kurtosis in the distribution, and we demonstrate that these non-Gaussian effects are a manifestation of asymmetry in relation to the resource theory of thermodynamics. Furthermore, we also show that the non-coherent and coherent contributions satisfy independently the Evans-Searles fluctuation theorem, which sets strong bounds on the statistics, with negative values of the dissipation being exponentially suppressed. Our findings are illustrated in a driven two-level system and an Ising chain, where quantum signatures of the work distribution in the macroscopic limit are discussed.
Highlights
The statistics of work, heat, and dissipation play a central role in the study of the nonequilibrium thermodynamics of small systems, both classical [1,2] and quantum [3,4,5]
V D, we review how the central limit theorem relates to our results, and we study the thermodynamic limit of an Ising chain, showing that despite the Gaussianity of the distribution, the breakdown of the fluctuation-dissipation relation (FDR) still witnesses the underlying quantum character of the process
We prove that the family of second laws of Ref. [23], accounting for the nonequilibrium resources in the energy spectrum, collapse into a single law in this regime, which only contributes with a Gaussian term to the probability distribution
Summary
The statistics of work, heat, and dissipation play a central role in the study of the nonequilibrium thermodynamics of small systems, both classical [1,2] and quantum [3,4,5]. [16] that a correction to Eq (1) is needed in order to account for the fluctuations arising from additional quantum uncertainty in the system This result implies that the probability distribution will deviate from a Gaussian whenever coherences are produced, meaning that one needs more information than the average wdiss to characterize p(w) even in the slow driving regime. The inverse temperature β of the environment is the same throughout
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