The simulated annealing (SA), and the Metropolis Algorithm (MA) before it, provide a means to simulate large ensembles of interacting entities using Markov Chain Monte Carlo (MCMC) simulation methods. The SA algorithm is often described as a meta–heuristic owing to its broad applicability to many types of optimization problems. In SA, a temperature control parameter t modifies the associated MCMC simulation over time so that optimal solutions having increasing probability of being sampled if t is decreased according to an appropriate cooling schedule. This paper describes a fundamental connection between these statistical mechanics algorithms and formal privacy frameworks such as differential privacy (DP). We propose a Boltzmann Machine Privacy Framework (BMPF) that entails application of a logistic acceptance function (as a proxy for the MA) and simulated annealing (denoted here as MA/SA) algorithms to unsolve optimization problems by sampling a Markov Chain at a fixed positive temperature using an objective function herein referred to as a consensus function. The only requirement for the consensus function other than that it operates on discrete values is that the ‘optimal’ solution must correspond to the ground-truth. Consequently, sub-optimal solutions sampled from the MCMC simulation at a positive temperature t> 0 corresponds to a noisy version of the ground truth. In addition to defining one of many possible consensus functions, we define a suitable configuration space and candidate generation scheme that maintains detailed balance in the Markov chain thereby ensuring convergence to a stationary distribution. A Boltzmann Machine Mechanism (BMM) is defined as the k-step transition probability of the Markov chain where the ground truth value is the initial state. We show that the BMPF satisfies the definition of approximate DP that converges to pure–DP as the number of iterations k →∞. This implies that the difference between the finite-time distribution and the stationary distribution of the Markov chain is bound up in the value of δ. We also prove that the value of ϵ in Approximate DP is related to the temperature parameter in the SA algorithm, i.e., ϵ(t) ≡ 2s/t where s corresponds to the sensitivity parameter for bounded neighbors. We apply this framework to histograms as a proof-of-concept.