Squeezing stationary distributions of stochastic chemical reaction systems

• URL: http://arxiv.org/abs/2209.08787v1
• Date: Mon, 19 Sep 2022 06:34:21 GMT
• Title: Squeezing stationary distributions of stochastic chemical reaction systems
• Authors: Yuji Hirono, Ryo Hanai
• Abstract summary: We show that product-form Poisson distributions correspond to coherent states in chemical reaction systems. A squeezed coherent state gives the transformed network, for which analytic expression is obtained.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Stochastic modeling of chemical reaction systems based on master equations has been an indispensable tool in physical sciences. In the long-time limit, the properties of these systems are characterized by stationary distributions of chemical master equations. In this paper, we describe a novel method for computing stationary distributions analytically, based on a parallel formalism between stochastic chemical reaction systems and second quantization. Anderson, Craciun, and Kurtz showed that, when the rate equation for a reaction network admits a complex-balanced steady-state solution, the corresponding stochastic reaction system has a stationary distribution of a product form of Poisson distributions. In a formulation of stochastic reaction systems using the language of second quantization initiated by Doi, product-form Poisson distributions correspond to coherent states. Pursuing this analogy further, we study the counterpart of squeezed states in stochastic reaction systems. Under the action of a squeeze operator, the time-evolution operator of the chemical master equation is transformed, and the resulting system describes a different reaction network, which does not admit a complex-balanced steady state. A squeezed coherent state gives the stationary distribution of the transformed network, for which analytic expression is obtained.

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