Entropy production and volume contraction in thermostated Hamiltonian dynamics

Maximum speed of dissipation

We derive statistical-mechanical speed limits on dissipation from the classical, chaotic dynamics of many-particle systems. In one, the rate of irreversible entropy production in the environment is the maximum speed of a deterministic system out of equilibrium, S[over ¯]_{e}/k_{B}≥1/2Δt, and its inverse is the minimum time to execute the process, Δt≥k_{B}/2S[over ¯]_{e}. Starting with deterministic fluctuation theorems, we show there is a corresponding class of speed limits for physical observables measuring dissipation rates. For example, in many-particle systems interacting with a deterministic thermostat, there is a trade-off between the time to evolve between states and the heat flux, Q[over ¯]Δt≥k_{B}T/2. These bounds constrain the relationship between dissipation and time during nonstationary processes, including transient excursions from steady states.

Rényi entropy yields artificial biases not in the data and incorrect updating due to the finite-size data

We show that the Rényi entropy implies artificial biases not warranted by the data and incorrect updating information due to the finite size of the data despite being additive. It is demonstrated that this is so because it does not conform to the system and subset independence axioms of Shore and Johnson [J. IEEE Trans. Inf. Theory 26, 26 (1980)IETTAW0018-944810.1109/TIT.1980.1056144]. We finally show that the escort averaged constraints do not remedy the situation.