Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userRelations between Heat Exchange and R{e}nyi Divergences
187
0
0.0
(
0
)
Authors
Bo-Bo Wei
Ask ChatGPT about the research
No Arabic abstract
In this work, we establish an exact relation which connects the heat exchange between two systems initialized in their thermodynamic equilibrium states at different temperatures and the R{e}nyi divergences between the initial thermodynamic equilibrium state and the final non-equilibrium state of the total system. The relation tells us that the various moments of the heat statistics are determined by the Renyi divergences between the initial equilibrium state and the final non-equilibrium state of the global system. In particular the average heat exchange is quantified by the relative entropy between the initial equilibrium state and the final non-equilibrium state of the global system. The relation is applicable to both finite classical systems and finite quantum systems.
rate research
Read More
We investigate monogamy relations related to the R{e}nyi-$alpha$ entanglement and polygamy relations related to the R{e}nyi-$alpha$ entanglement of assistance. We present new entanglement monogamy relations satisfied by the $mu$-th power of R{e}nyi-$alpha$ entanglement with $alphain[sqrt{7}-1)/2,(sqrt{13}-1)/2]$ for $mugeqslant2$, and polygamy relations satisfied by the $mu$-th power of R{e}nyi-$alpha$ entanglement of assistance with $alphain[sqrt{7}-1)/2,(sqrt{13}-1)/2]$ for $0leqmuleq1$. These relations are shown to be tighter than the existing ones.
Thermodynamics and information theory have been intimately related since the times of Maxwell and Boltzmann. Recently it was shown that the dissipated work in an arbitrary non-equilibrium process is related to the R{e}nyi divergences between two states along the forward and reversed dynamics. Here we show that the relation between dissipated work and Renyi divergences generalizes to $mathcal{PT}$-symmetric quantum mechanics with unbroken $mathcal{PT}$ symmetry. In the regime of broken $mathcal{PT}$ symmetry, the relation between dissipated work and Renyi divergences does not hold as the norm is not preserved during the dynamics. This finding is illustrated for an experimentally relevant system of two-coupled cavities.
In this work, we investigate the heat exchange between two quantum systems whose initial equilibrium states are described by the generalized Gibbs ensemble. First, we generalize the fluctuation relations for heat exchange discovered by Jarzynski and Wojcik to quantum systems prepared in the equilibrium states described by the generalized Gibbs ensemble at different generalized temperatures. Second, we extend the connections between heat exchange and Renyi divergences to quantum systems with very general initial conditions.These relations are applicable for quantum systems with conserved quantities and are universally valid for quantum systems in the integrable and chaotic regimes.
We investigate monogamy relations and upper bounds for generalized $W$-class states related to the R{e}nyi-$alpha$ entropy. First, we present an analytical formula on R{e}nyi-$alpha$ entanglement (R$alpha$E) and R{e}nyi-$alpha$ entanglement of assistance (REoA) of a reduced density matrix for a generalized $W$-class states. According to the analytical formula, we show monogamy and polygamy relations for generalized $W$-class states in terms of R$alpha$E and REoA. Then we give the upper bounds for generalized $W$-class states in terms of R$alpha$E. Next, we provide tighter monogamy relations for generalized $W$-class states in terms of concurrence and convex-roof extended negativity and obtain the monogamy relations for R$alpha$E by the analytical expression between R$alpha$E and concurrence. Finally, we apply our results into quantum games and present a new bound of the nonclassicality of quantum games restricting to generalized $W$-class states.
The R{e}nyi and von Neumann entropies of various bipartite Gaussian states are derived analytically. We also discuss on the tripartite purification for the bipartite states when some particular conditions hold. The generalization to non-Gaussian states is briefly discussed.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
