Irreversibility and entropy (original) (raw)

Entropy production in a non-Markovian environment

Physical Review E, 2015

Stochastic thermodynamics and the associated fluctuation relations provide means to extend the fundamental laws of thermodynamics to small scales and systems out of equilibrium. The fluctuating thermodynamic variables are usually treated in the context of isolated Hamiltonian evolution, or Markovian dynamics in open systems. In this work we introduce an explicitly non-Markovian model of dynamics of an open system, where the correlations between the system and the environment drive a subset of the environment outside of equilibrium. This allows us to identify the non-Markovian sources of entropy production. We show that the non-Markovian components lead to modifications in the standard fluctuation relations for entropy. As a concrete example, we explicitly derive such modified fluctuation relations for the case of an overheated single electron box.

Intrinsic irreversibility of Kolmogorov dynamical systems

Physica A-statistical Mechanics and Its Applications, 1983

We give the mathematical details and various extensions of the results stated in previous work of Courbage and Prigogine. "Intrinsic random systems" are deterministic and conservative dynamical systems for which we can associate two dissipative Markov processes through a one-to-one "change of representation", the first leading to equilibrium for t -++cc and the second for r-+-co.

Entropy and global Markov properties

Communications in Mathematical Physics, 1990

We extend, refine and give simple proofs of some recent results on the validity of global Markov properties for classical spin systems. One of the new results is that there is a global Markov property that is satisfied by equilibrium states in general. The proof of this establishes formulas for the entropy and free energy that show that these quantities are, for d-dimensional systems, given in terms of (d -l)-dimensional systems. Furthermore, we show that global Markov properties imply the absence of some types of symmetry breaking.

Non-Markovian Dynamics Impact on the Foundations of Statistical Mechanics

The foundations of statistical mechanics, namely how equilibrium hypothesis emerges microscopically from quantum theory, is explored through investigating the environment-induced quantum decoherence processes. Based on the recent results on non-Markovian dynamics [Phys. Rev. Lett. 109, 170402 (2012)], we find that decoherence of quantum states manifests unexpected complexities. Indeed, an arbitrary given initial quantum state, under the influence of different reservoirs, can evolve into four different steady states: thermal, thermal-like, quantum memory and oscillating quantum memory states. The first two steady states \textit{de facto} provided a rigorous proof how the system relaxes to thermal equilibrium with its environment. The latter two steady states, with strong non-Markovian effects, will maintain the initial state information and not reach thermal equilibrium, which is beyond the conventional wisdom of statistical mechanics.