017_20160826 thermodynamics of stochastic turing machines

Thermodynamic Of Stochastic Turing Machines

Tran Quoc Hoan

@k09ht haduonght.wordpress.com/

Paper Alert 2016-08-26, Hasegawa lab., Tokyo

The University of Tokyo

Philipp Strasberg, Javier Cerrillo, Gernot Schaller, and Tobias Brandes, Phys. Rev. E 92, 042104 – Published 5 October 2015

Findings

Thermodynamic Of Stochastic Turing Machines 2

• Show how to construct stochastic models which mimic the behavior of a general-purpose computer (a Turing machine).

• Discrete state systems obeying a Markovian master equation, which are logically reversible and have a well-defined and consistent thermodynamic interpretation

使うどころはよくわからん！！！

Turing Machines


Computation T: scan from left most blank cell to right most blank cell

State

Symbol Direction0,+1,-1

Halting problem: It is impossible to design a TM TH which tells us for an arbitrary given TM T and input s whether (T,S) will halt or not

TM

Stochastic Turing Machines


Logically reversible computer:

principle able to unambiguously retrace its computational path back to the initial state.

Logically reversible Turing machine


Based on idea of Bennett (1973)

4 tapes: input, working, history, output



Step 1: Copy input into working tape

(state, input, working)



Step 2: Compute

(state, working, history)



Step 3: Copy output (in working tape) to output tape

(state, working, output)



Step 4: Retrace computation

(state, working, history)

-> the working tape contains input again and the history tape is returned

to blank



Step 5: Erase working tape (state, input, working)

Stochastic Turing machine


• Use a continuous-time Markov process to model any logically reversible TM, simply called as stochastic TM

Thermodynamic of Brownian computation


Approximate master eqn. by Fokker-Planck eqn.

Thinking about when stochastic approximate deterministic


Thermodynamic Of Stochastic Turing Machines 13Not imply that total integrated

entropy is zero



Q: How about efficiency of thermodynamic computer?

017_20160826 thermodynamics of stochastic turing machines

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