# Exact correspondence between Renyi entropy flows and physical flows

@article{Ansari2015ExactCB, title={Exact correspondence between Renyi entropy flows and physical flows}, author={Mohammad H. Ansari and Yuli V. Nazarov}, journal={Physical Review B}, year={2015}, volume={91}, pages={174307} }

We present a universal relation between the flow of a Renyi entropy and the full counting statistics of energy transfers. We prove the exact relation for a flow to a system in thermal equilibrium that is weakly coupled to an arbitrary time-dependent and nonequilibrium system. The exact correspondence, given by this relation, provides a simple protocol to quantify the flows of Shannon and Renyi entropies from the measurements of energy transfer statistics.

## 21 Citations

Strong correlations between the exponent α and the particle number for a Renyi monoatomic gas in Gibbs' statistical mechanics.

- PhysicsPhysical review. E
- 2017

It is shown that already at the classical level there is a strong correlation between Renyi's exponent α and the number of particles for very simple systems.

Troublesome aspects of the Renyi-MaxEnt treatment.

- Computer SciencePhysical review. E
- 2016

A hidden relation is uncovered in Renyi's variational problem (MaxEnt) that connects the two associated Lagrange multipliers with the mean energy 〈U〉 and the Renyi parameter α and produces anomalous Renyi-MaxEnt thermodynamic results.

Optimum capacity and full counting statistics of information content and heat quantity in the steady state

- PhysicsPhysical Review B
- 2019

The performance of communication through a quantum conductor is limited by the laws of physics. The optimum channel capacity, the maximum rate at which information can be transmitted under a given…

Fluctuation of information content and the optimum capacity for bosonic transport

- Physics, Computer Science
- 2021

The Renyi entanglement entropy of order zero is the partition function, which exponentially depends on the optimum capacity, and the water-filling theorem is recovered in the wave-like regime.

Full counting statistics of information content

- PhysicsThe European Physical Journal Special Topics
- 2019

We review connections between the cumulant generating function of full counting statistics of particle number and the Rényi entanglement entropy. We calculate these quantities based on the fermionic…

Dimensional regularization of Renyi’s statistical mechanics

- PhysicsPhysica A: Statistical Mechanics and its Applications
- 2018

Full counting statistics of information content and particle number

- Physics, Computer Science
- 2017

This work considers a bipartite quantum conductor and discusses the joint probability distribution of particle number in a subsystem and the self-information associated with the reduced density matrix of the subsystem, and calculates the Renyi entropy of a positive integer order subjected to the particle number constraint.

Reciprocity relations and generalized, classic entropic quantifiers that lack trace-form

- Computer SciencePhysica A: Statistical Mechanics and its Applications
- 2019

A nonlinear matter-field Hamiltonian analyzed with Renyi and Tsallis statistics

- Computer Science
- 2019

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