A Second Law for Open Markov Processes

Abstract

In this paper we define the notion of an open Markov process. An open Markov process is a generalization of an ordinary Markov process in which populations are allowed to flow in and out of the system at certain boundary states. We show that the rate of change of relative entropy in an open Markov process is less than or equal to the flow of relative entropy through its boundary states. This can be viewed as a generalization of the Second Law for open Markov processes. In the case of a Markov process whose equilibrium obeys detailed balance, this inequality puts an upper bound on the rate of change of the free energy for any non-equilibrium distribution.

9 pages, 3 figures

References in corpus (1)

• Data processing theorems and the second law of thermodynamics

Cited by in corpus (4)

• The thermodynamic efficiency of computations made in cells across the range of life
• Dependence of dissipation on the initial distribution over states
• The free energy requirements of biological organisms; implications for evolution
• Open Markov processes: A compositional perspective on non-equilibrium steady states in biology