Dependence of dissipation on the initial distribution over states

Abstract

We analyze how the amount of work dissipated by a fixed nonequilibrium process depends on the initial distribution over states. Specifically, we compare the amount of dissipation when the process is used with some specified initial distribution to the minimal amount of dissipation possible for any initial distribution. We show that the difference between those two amounts of dissipation is given by a simple information-theoretic function that depends only on the initial and final state distributions. Crucially, this difference is independent of the details of the process relating those distributions. We then consider how dissipation depends on the initial distribution for a 'computer', i.e., a nonequilibrium process whose dynamics over coarse-grained macrostates implement some desired input-output map. We show that our results still apply when stated in terms of distributions over the computer's coarse-grained macrostates. This can be viewed as a novel thermodynamic cost of computation, reflecting changes in the distribution over inputs rather than the logical dynamics of the computation.

References in corpus (9)

• Dissipation: The phase-space perspective
• Optimal finite-time processes in stochastic thermodynamics
• Rare events and the convergence of exponentially averaged work values
• Work and information processing in a solvable model of Maxwell's demon
• The thermodynamics of prediction
• Path-integral analysis of fluctuation theorems for general Langevin processes
• The "footprints'' of irreversibility
• The free energy requirements of biological organisms; implications for evolution
• Work fluctuation and total entropy production in nonequilibrium processes

Cited by in corpus (22)

• Stochastic thermodynamics of computation
• Thermodynamics of computing with circuits
• Is stochastic thermodynamics the key to understanding the energy costs of computation?
• Thermodynamic costs of Turing Machines
• Initial-State Dependence of Thermodynamic Dissipation for any Quantum Process
• Thermodynamics and computation during collective motion near criticality
• Number of hidden states needed to physically implement a given conditional distribution
• Thermodynamics of computations with absolute irreversibility, unidirectional transitions, and stochastic computation times
• A space-time tradeoff for implementing a function with master equation dynamics
• The impossibility of Landauer's bound for almost every quantum state
• Landauer Principle and Thermodynamics of Computation
• Balancing Error and Dissipation in Computing
• Dependence of integrated, instantaneous, and fluctuating entropy production on the initial state in quantum and classical processes
• Refining Landauer's Stack: Balancing Error and Dissipation When Erasing Information
• Biochemical Szilard engines for memory-limited inference
• Maximizing free energy gain
• Nonequilibrium thermodynamics of uncertain stochastic processes
• Entropy production given constraints on the energy functions
• Generalized Zurek's bound on the cost of an individual classical or quantum computation
• Minimal thermodynamic cost of communication
• First and Second Laws of Information Processing by Nonequilibrium Dynamical States
• Energetic advantages for quantum agents in online execution of complex strategies