# Equilibrium and Termination

@inproceedings{Danos2010EquilibriumAT, title={Equilibrium and Termination}, author={Vincent Danos and Nicolas Oury}, booktitle={DCM}, year={2010} }

We present a reduction of the termination problem for a Turing machine (in the simplified form of the Post correspondence problem) to the problem of determining whether a continuous-time Markov chain presented as a set of Kappa graph-rewriting rules has an equilibrium. It follows that the problem of whether a computable CTMC is dissipative (ie does not have an equilibrium) is undecidable.

## 6 Citations

### Equilibrium and Termination ( extended version ) ∗

- Economics
- 2011

We present a reduction of the Post correspondence problem (PCP) to the question of whether a continuous-time Markov chain (CTMC) presented as a set graph-rewriting rules has an equilibrium. It…

### Equilibrium and termination II: the case of Petri nets

- MathematicsMathematical Structures in Computer Science
- 2013

A simple algebraic criterion is established for the existence of an equilibrium that satisfies the detailed balance condition familiar from the thermodynamics of reaction networks and it is found that when such a probability exists, it can be described by a free energy function that combines an internal energy term and an entropy term.

### On the Statistical Thermodynamics of Reversible Communicating Processes

- Computer ScienceCALCO
- 2011

A lower bound on energy costs is found which guarantees that a process converges to a probabilistic equilibrium state (a grand canonical ensemble in statistical physics terms) and implies that such processes hit a success state in finite average time, if there is one.

### Thermodynamic Graph-Rewriting

- MathematicsCONCUR
- 2013

A new thermodynamic approach to stochastic graph-rewriting, where the generators define the qualitative dynamics, by showing which transformations are possible, while the energy patterns and cost function specify the long-term probability of any reachable graph.

### Cooperative Assembly Systems

- Materials ScienceDNA
- 2011

The phase transition structure of a class of bipartite cooperative assembly systems is investigated and which of these systems have a (probabilistic) equilibrium and find an explicit form for their local energy is characterized.

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